One word in one verse does NOT determine the meaning of a word. Here are ten vss. where Jesus, Himself, defined/described "aionios" as eternal/everlasting/for ever etc.
…..Some people claim that “aion/aionios” never means eternity/eternal because they sometimes refer to things which are not eternal.
However, neither word is ever defined/described, by other adjectives or descriptive phrases, as meaning a period of time less than eternal, in the New Testament, as in the following verses.
…..Jesus used “aionios” twenty eight [28] times. He never used “aionios” to refer to anything ordinary or mundane that was not or could not be eternal.
…..In the following verses Jesus defines “aionios” as “eternal.”
[1] Luke 1:33
(33) And he shall reign [basileusei][Vb] over the house of Jacob for ever; [aionas] and of his kingdom [basileias][Nn] there shall be no end.[telos]
In this verse the reign/basileusei, which is the verb form of the word, is "aionas" and of the kingdom/basileias, the noun form of the same word, "there shall be no end.” “Aionas” by definition means eternal.
[2] John 6:58
(58) This is the bread that came down from heaven. Your ancestors ate manna and died, but whoever feeds on this bread will live forever.[aionios]
In this verse Jesus juxtaposes “aionios life” with “death.” If “live aionios” is only a finite period, a finite period is not opposite “death.” Thus “aionios” by definition means “eternal.”
[3] John 10:28
(28) I give them eternal [aionios] life, and they shall never [aion] perish; no one will snatch them out of my hand.
In this verse Jesus parallels “aionios” and “aion” with “[not] snatch them out of my hand.” If “aion/aionios” means “age(s), a finite period,” that is not the opposite of “[not] snatch them out of my hand’” “Aionios life” by definition means “eternal life.”
[4]John 3:15
(15) That whosoever believeth in him should not perish, but have eternal [aionion] life.
[5] John 3:16
(16) For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting [aionion] life.
In these two verses Jesus parallels “aionion life” with “should not perish.” Believers could eventually perish in a finite period, thus by definition “aionion life” here means eternal or everlasting life.
[6]John 5:24
(24) Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting [aionios] life, and shall not come into condemnation; but is passed from death unto life.
In this verse Jesus parallels “aionios” with “shall not come into condemnation” and “passed from death unto life.” “Aionios” does not mean “a finite period,” by definition here it means “eternal,” unless Jesus lets His followers come into condemnation and pass into death.
[7]John 3:36 He that believeth on the Son hath everlasting [aionios] life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
In this verse Jesus juxtaposed aionios life with “shall not see life.” If aionios means an indefinite age that is not opposite “shall not see life” By definition aionios means eternal.
[8]John 4:14 But whosoever drinketh of the water that I shall give him shall never [ου μη/ou mé] thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting [aionios] life.
In this verse Jesus paralleled aionios with “shall [ου μη/ou mé][fn] never thirst.” If aionios means an indefinite age that is not opposite “shall never thirst.” By definition aionios means eternal. See footnote [fn] on “ou mé” below.
[9]John 6:27
(27) Labour not for the meat which perisheth, but for that meat which endureth unto everlasting [aionios] life, which the Son of man shall give unto you: for him hath God the Father sealed.
In this verse Jesus contrasted “aionios meat” with “meat that perishes” If aionios means an indefinite age that is not opposite “meat that perishes.” By definition aionios means eternal.
[10]John 8:51
(51) Very truly [amen amen] I tell you, whoever obeys my word will never [ou mé eis ton aiona][fn] see death."
In this verse Jesus juxtaposes “unto aion” with “never see death.” By definition “aion” means eternity.
You haven't taken Luke 1 out of that cut and paste list yet? I've already shown several times that that passage doesn't prove your point. But, since you posted it again, I'll show it again. Here is what you said concerning Luke 1
"In this verse the reign/basileusei, which is the verb form of the word, is "aionas" and of the kingdom/basileias, the noun form of the same word, "there shall be no end.” “Aionas” by definition means eternal."
Your argument is, since the kingdom shall have no end, His reign, (aionios) must also have no end. However, that is not the case as we see from Scripture. Jesus doesn't reign forever.
22 For as in Adam all die, even so in Christ shall all be made alive. 23 But every man in his own order: Christ the firstfruits; afterward they that are Christ’s at his coming. 24
Then cometh the end, when he shall have delivered up the kingdom to God, even the Father; when he shall have put down all rule and all authority and power. 25 For he must reign, till he hath put all enemies under his feet. 26 The last enemy that shall be tdestroyed is death. 27 For he hath put all things under his feet. But when he saith, all things are put under him, it is manifest that he is excepted, which did put all things under him. 28 And when all things shall be subdued unto him,
then shall the Son also himself be subject unto him that put all things under him, that God may be all in all
The Holy Bible: King James Version, Electronic Edition of the 1900 Authorized Version. (Bellingham, WA: Logos Research Systems, Inc., 2009), 1 Co 15:22–28.
We see here that Paul tells us that in the end, Jesus will deliver the kingdom over to the Father. Then Jesus Himself will be subject to the Father. So, we see that the Kingdom has no end. However, Jesus doesn't reign over it for eternity. Thus, Luke 1 does not make your point.
considering the other passages, I didn't see anywhere that Jesus said aionios means eternal. It seems to me that you're trying to use those passages to "reason" aion to fit your meaning.