Question: Are there different types of perfection according to Paul? 1 Corinthians 13:10, Philippians 3:12, 2 Timothy 3:17 & Ephesians 4:13
Complete
If we grant that (in the Greek words used) "perfect" and "complete" carry the same meaning, Paul is simply referring to different entities becoming "complete".
(3 of the 4 passages contain forms of τέλειος, and 2 Tim uses the somewhat-but-not-quite synonymous ἄρτιος, both of which can be translated as "perfect" or "complete")
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Knowledge
In 1 Cor 13 Paul speaks of knowledge becoming complete (see vss. 9,12).
Although the timing is not given, the reference to face-to-face suggests a future appearance before God (judgment day?), and the passage echoes the thoughts of the millennarian prophecy in Isaiah 11:9, see also Habakkuk 2:14)
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Paul himself
Paul acknowledges in Philippians that he is a work in progress. God has called him to be something more and will help him get there, but the master craftsman isn't done working on Paul just yet.
Paul appears (here & elsewhere) to have in mind a prize beyond this life.
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The work of the kingdom
Paul suggests that the scriptures equip people for the work God intends them to do--note that the verb ἐξαρτίζω is used in parallel with the adjective ἄρτιος, suggesting the man who avails himself of the scriptures will be fully equipped.
There is no need to suggest that this level of preparedness is beyond mortal reach.
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The church
Paul speaks of the body of Christ attaining a state of perfection or completion, and that God has given tools to get them there, but they aren't there yet. This passage could be read as a response to the question "why do we need apostles & teachers?".
If we accept the NT symbolism that the church is the bride being prepared for the bridegroom (similar motifs are found in the OT), and the wedding is at or after a future coming of Christ, this hasn't happened yet either.
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Conclusion
Various people/entities can become complete in different ways. Paul speaks of most of these processes of development as things that are still a work-in-progress.
Lest we try to water-down the weight of "perfection" too much though, consider the following thought experiment:
Let's say God sets some very high standard ("perfection", "completion") for where He wants His children to be. The exact height of the standard is irrelevant to the thought experiment, as long as we are aware that it's beyond anything we'll get to in a ~75 year mortal sojourn. Does this mean we'll never reach that standard?
Hardly. For those willing to fully embrace
not my will but Thine be done: if Almighty God has all eternity to work with them, why in the world wouldn't He be able to get them to goal He has set?