Here is the definition of Kolasis from BDAG one of, if not, the most highly accredited lexicons available. The blue indicates the many sources the authors used to determine the meaning. "Punishment" not "correction."
BDAG makes references to "chastisement" which can certainly be corrective. Synonyms of "chastisement" given by Webster's dictionary are "castigate, chasten, correct, discipline, penalize, punish". For the verb, kolazo, BDAG admits to "Aristotle's limitation of the term...to disciplinary action" which Danker opines is "not reflected in general usage" (p.555).
κόλασις, εως, ἡ (s. prec. three entries;
‘punishment, chastisement’ so Hippocr.+; Diod S 1, 77, 9; 4, 44, 3; Aelian, VH 7, 15; SIG2 680, 13; LXX; TestAbr, Test12Patr, ApcEsdr, ApcSed; AscIs 3:13; Philo, Leg. ad Gai. 7, Mos. 1, 96; Jos., Ant. 17, 164; SibOr 5, 388; Ar. [Milne 76, 43]; Just.)
① infliction of suffering or pain in chastisement, punishment so lit. κ. ὑπομένειν undergo punishment Ox 840, 6; δειναὶ κ. (4 Macc 8:9) MPol 2:4; ἡ ἐπίμονος κ. long-continued torture ibid. Of the martyrdom of Jesus (Orig., C. Cels. 1, 48, 95; 8, 43, 12) PtK 4 p. 15, 34. The smelling of the odor arising fr. sacrifices by polytheists ironically described as punishment, injury (s. κολάζω) Dg 2:9.
② transcendent retribution, punishment (ApcSed 4:1 κόλασις καὶ πῦρ ἐστιν ἡ παίδευσίς σου.—Diod S 3, 61, 5; 16, 61, 1; Epict. 3, 11, 1; Dio Chrys. 80 [30], 12; 2 Macc 4:38 al. in LXX; Philo, Spec. Leg. 1, 55; 2, 196; Jos., Ant. 1, 60 al.; Just.; Did., Gen., 115, 28; 158, 10) ApcPt 17:32; w. αἰκισμός 1 Cl 11:1. Of eternal punishment (w. θάνατος) Dg 9:2 (Diod S 8, 15, 1 κ. ἀθάνατος). Of hell: τόπος κολάσεως ApcPt 6:21 (Simplicius in Epict. p. 13, 1 εἰς ἐκεῖνον τὸν τόπον αἱ κολάσεως δεόμεναι ψυχαὶ καταπέμπονται); ἐν τῇ κ. ἐκείνῃ 10:25; ibid. ἐφορῶσαι τὴν κ. ἐκείνων (cp. ApcEsdr 5:10 p. 30, 2 Tdf. ἐν τῇ κ.). ἐκ τῆς κ. ApcPt Rainer (cp. ἐκ τὴν κ. ApcSed 8:12a; εἰς τὴν κ. 12b and TestAbr B 11 p. 116, 10 [Stone p. 80]). ἀπέρχεσθαι εἰς κ. αἰώνιον go away into eternal punishment Mt 25:46 (οἱ τῆς κ. ἄξιοι ἀπελεύσονται εἰς αὐτήν Iren. 2, 33, 5 [Harv. I 380, 8]; κ. αἰώνιον as TestAbr A 11 p. 90, 7f [Stone p. 28]; TestReub 5:5; TestGad 7:5; Just., A I, 8, 4; D. 117, 3; Celsus 8, 48; pl. Theoph. Ant. 1, 14 [p. 90, 13]). ῥύεσθαι ἐκ τῆς αἰωνίου κ. rescue fr. eternal punishment 2 Cl 6:7. τὴν αἰώνιον κ. ἐξαγοράζεσθαι buy one’s freedom fr. eternal pun. MPol 2:3 v.l. κακαὶ κ. τοῦ διαβόλου IRo 5:3. κ. τινος punishment for someth. (Ezk 14:3, 7; 18:30; Philo, Fuga 65 ἁμαρτημάτων κ.) ἔχειν κόλασίν τινα τῆς πονηρίας αὐτοῦ Hs 9, 18, 1. ἀναπαύστως ἕξουσιν τὴν κ. they will suffer unending punishment ApcPt Bodl. 9–12. ὁ φόβος κόλασιν ἔχει fear has to do with punishment 1J 4:18 (cp. Philo, In Flacc. 96 φόβος κολάσεως).—M-M. TW.
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 555). Chicago: University of Chicago Press.
The Universalist position on NT usage of these words is that in contexts where such words occur (e.g. Mt.25:46; 2 Pet.2:9), in reference to Divinely given eschatological &/or postmortem punishment, they are not indicative of vindictive retributive punishment, but rather of a corrective punishing or chastening for the good of the offender.
The following sources allege that the words under consideration were used of corrective punishment before, soon after & at the time of Christ.
According to this alleged quote of Trench κόλασις, as opposed to τιμωρία, has "more the notion of punishment as it has reference to the correction and bettering of the offender (see Philo, Leg, ad Cai. I; Josephus, Antt. ii. 6. 8); it is ‘castigatio,’ and naturally has for the most part a milder use than τιμωρία. Thus Plato (Protag. 323 e) joins κολάσεις and νουθετήσεις together: and the whole passage to the end of the chapter is eminently instructive as to the distinction between the words: οὐδεὶς κολάζει τοὺς ἀδικοῦντας ὅτι ἠδίκησεν, ὅστις μὴ ὥσπερ θηρίον ἀλογίστως τιμωρεῖται, ... ἀλλὰ τοῦ μέλλοντος χάριν ἵνα μὴ αὖθις ἀδικήσῃ; the same change in the words which he employs, occurring again twice or thrice in the sentence; with all which may be compared what Clement of Alexandria has said, Strom. iv. 24; and again vii. 16, where he defines κολάσεις as μερικαὶ παιδεῖαι, and τιμωρία as κακοῦ ἀνταπόδοσις. And this is Aristotle’s distinction (Rhet. i. 10): διαφέρει δὲ τιμωρία καὶ κόλασις· ἡ μὲν γὰρ κόλασις τοῦ πάσχοντος ἕνεκά ἐστιν· ἡ δὲ τιμωρία, τοῦ ποιοῦντος, ἵνα ἀποπληρωθῇ: cf. Ethic. Nic. iv. 5: τιμωρία παύει τῆς ὀργῆς, ἠδονῆν ἀντὶ τῆς λύπης ἐμποιοῦσα. It is to these and similar definitions that Aulus Gellius refers when he says (Noct. Att. vi. 14): ‘Puniendis peccatis tres esse debere causas existimatum est. Una est quae νουθεσία, vel, κόλασις, vel παραίνεσις dicitur; cum poena adhibetur castigandi atque emendandi gratiâ; ut is qui fortuito deliquit, attentior fiat, correctiorque. Altera est quam ii, qui vocabula ista curiosius diviserunt, τιμωρίαν appellant. Ea causa animadvertendi est, cum dignitas auctoritasque ejus, in quem est peccatum, tuenda est, ne praetermissa animadversio contemtum ejus pariat, et honorem levet: idcircoque id ei vocabulum a conservatione honoris factum putant.’ There is a profound commentary on these words in Göschel’s Zerstreute Blätter, part 2, p. 343–360; compare too an instructive note in Wyttenbach’s Animadd. in Plutarch. vol. xii. p. 776."
https://www.blueletterbible.org/lang/trench/section.cfm?sectionID=7
So in favor of κόλασις (or κολάζω) being corrective Trench lists quotes from Plato, Aristotle, Philo, Josephus, Aulus Gellius & Clement of Alexandria. To those we could add early church universalists such as Oregon, Gregory Nyssa & many others. Moulton & Milligan continue to add to that list as follows:
"The meaning ";cut short,"; which the presumable connexion with κόλος and κολούω would suggest, seems to be the original sense of the word. In the Paris Thesaurus we find quotations for the meaning ";prune"; (κόλασις τῶν δένδρων), and a number of late passages where the verb denotes ";correcting,"; ";cutting down"; a superfluity. Thus Galen ad Galatians 1:1-24 τὰ γὰρ ἐναντία τῶν ἐναντίων ἰάματά ἐστι, κολάζοντα μὲν τὸ ὑπερβάλλον. Of course this may be a derived sense, like that of castigo and of our ";correct,"; but in any case it is clearly a familiar sense during the NT period, and we cannot leave it out of consideration when we examine this very important word."
https://www.studylight.org/lexicons/greek/2849.html
In addition to those, under the section on κολάζω in TDNT, J. Schneider notes regarding "inscr. given by Steinleitner from Phrygian and Lydian monuments of the imperial period" that in "these inscriptions the sins punished by deity are those against the deity itself, e.g. violations of the sacred cultic laws. The deity smites the offender with sickness and infirmity, or even punishes himself and his family with death. The sinner can win back the grace of the deity only by open confession of his guilt. In this way alone can he be liberated from sickness and misfortune."
TDNT adds regarding Philo's view of the "legislative power of God" that this "power divides into two branches, the one for the rewarding of the good and the other for the punishment of sinners. Philo's view of God includes the insight that in God mercy is older than punishment (Deus Imm.,76) and that God would rather forgive than punish (Spec.Leg., II,196...). Punishment is for those who are not amenable to reason (Agric.,40). Thus punishment may seem to be the greatest evil, but it is to be regarded as the greatest blessing for fools, loc. cit. This is a Stoic view" ("Theological Dictionary of the New Testament", TDNT, ed. G. Kittel, Vol.3, p.815).
The "New International Dictionary of New Testament Theology and Exegesis" (NIDNTTE, ed. Moises Silva, 2014, Vol. II, p.716-718) concurs with TDNT's remarks above.
NIDTTE also refers to the 5 NT occurrences of the "derived vb. κολαφίζω" (kolaphizo, Strongs # 2852), "to strike (with the fist), fig. torment". It is used twice of "the Jewish leaders who struck Jesus during his trial before the Sanhedrin (Matt 26:67 = Mark 14:65)." (NIDTTE, p.718).
"Then they spat in His face and beat Him with their fists; and others slapped Him," (Mt.26:67; NASB).
There are no indications of an intent to correct Jesus via such actions by these evil human beings. Rather it seems vindictive or sadistic. Likewise with the occurrences of kolaphizo at 1 Pet.2:20 & 1 Cor.4:11, does the "buffeting" or ""to strike (with the fist), fig. torment" have no hint of correction.
In all 4 cases of kolaphizo mentioned so far, they all are at the hands of men & do not indicate a corrective or beneficial purpose to those receiving such "torments". However, in the 5th occurrence of this word in the New Testament, that changes.
In 2 Cor.12:7 is the only one of the 5 that refer to a Divinely given kolaphizo (compare Mt.25:46). In this context the Lord gives Paul a thorn in the flesh to "torment" or "buffet" [κολαφίζῃ] him, not as a sadistic or vindictive retribution with no thought of benefit to Paul, but rather for Paul's own good:
"7 And lest I should be exalted above measure through the abundance of the revelations, there was given to me a thorn in the flesh, the messenger of Satan to buffet me, lest I should be exalted above measure. 8 For this thing I besought the Lord thrice, that it might depart from me. 9 And he said unto me, My grace is sufficient for thee: for my strength is made perfect in weakness. Most gladly therefore will I rather glory in my infirmities, that the power of Christ may rest upon me. 10 Therefore I take pleasure in infirmities, in reproaches, in necessities, in persecutions, in distresses for Christ's sake: for when I am weak, then am I strong."
In Matthew 25:46, like 2 Cor.12:7, is another New Testament instance of Divinely given sufferings, usually translated "punishment" (κόλασιν) (v.46) of "fire" (v.41). Shall it not also be, as the Divinely given sufferings of 2 Cor.12:7, for the good of the recipients?
Clearly the words under consideration are not always used of correction. So in order to determine whether or not their usage in eschatological and/or postmortem passages like Matthew 25:46 & 2 Peter 2:9 is corrective, one must consider the contexts. In that light, therefore, it seems questionable what use there would be in an examination of all of the many ancient Greek occurrences of the words. Will they inform us of the view of the New Testament God of love in regard to how He interprets them in an eschatological context? Or do extrabiblical usages, such as you've cited above, often come under the classification of false gods, fables & myths which are to be rejected, as in:
"Not giving heed to Jewish myths, and commandments of men, that turn from the truth." (Titus 1:14).
2 Timothy 4:4: And they shall turn away their ears from the truth, and shall be turned unto fables.
Do we find out what the real - good - God thinks on a subject by studying what the - evil - false gods think about it? Or how - evil - revengeful, bitter men with sadistic motivations use the words in question? They will punish from their own - evil - motives, whereas the - good - God, Love Omnipotent, always does so from the motive of the betterment of His created beings.
In support of that there is much to be brought forth from the inspired Scriptures & nothing in opposition to it. There are examples where His wrath, destruction, wounding, punishment, anger and torments are intended for the good of those who receive such. And no examples to the contrary.
Mat 18:34 And his lord was wroth, and delivered him to the tormentors, till he should pay all that was due unto him.
Matthew 25:46: “And these shall be coming away into chastening(kolasin) eonian, yet the just into life eonian.” (CLV)...1 John 4:18: “for fear has chastening(kolasin).” (CLV)
The servant who knows the master’s will and does not get ready or does not do what the master wants will be beaten with many blows. But the one who does not know and does things deserving punishment will be beaten with few blows. Luke 12:47-48a
https://www.tentmaker.org/books/hope_beyond_hell.pdf