What does the word “Punishment” mean in the Bible?

I’m by no means a Greek scholar, but with the inception of the internet, we can find reputable sources to locate and contemplate concordance definitions of what was meant in the original language in a matter of moments.
One such word I’ve felt drawn to know more of the meaning behind is: punishment.
Biblehub has concordance extracts conveniently located on one page where multiple viewpoints can be assessed.
Looking up “punishment” yielded the following results (extracted to simplify):

Englishman’s Concordance
2 occurrences: Matt 25:46 and 1 John 4:18
Strong’s Concordance
kolasis: correction
Original Word: κόλασις
HELPS Word-studies
Cognate: 2851 kólasis (from kolaphos, “a buffeting, a blow”) – properly, punishment that “fits” (matches) the one punished (R. Trench)
NAS Exhaustive Concordance
Word Origin:from kolazó
Definition: correction
Thayer’s Greek Lexicon
STRONGS NT 2851: κόλασις
the noted definition of Aristotle, which distinguishes κόλασις (kólasis) from τιμωρία (timóriaas that which (is disciplinary and) has reference to him who suffers, while the latter (is penal and) has reference to the satisfaction of him who inflicts
To state it simply, the Greek word for punishment (kólasis) applied as a penalty that fits the crime, a correction, and is for the benefit of the one being punished, not the one doing the punishing. Even in the Old Testament, the punishment fit the crime (i.e. eye for an eye). In other words, if this corrective punishment is for God’s benefit, τιμωρία (timória) would have been used. What sense would it make to have a corrective punishment if the person is never given the opportunity afterwards to live out the correction?
(Note: The word timória is used in Hebrews 10:29 but in a different fashion which would be a different topic for discussion. In short, that passage is directed towards Israel’s rejection of Jesus and the coming destruction via the Romans in 70AD in my opinion. It is speaking of punishment by death in this life, but not a “timória” punishment in the afterlife.)
So this brings up another question, what’s the deal with the word eternal? This is probably where most of the confusion comes in and could be a post or three of its own. It’s easy to understand a corrective punishment, but an everlasting correction is confusing depending on how it’s presented. It can be presented as burning forever in hell or as a corrective and permanent burning away of sinfulness.
The Greek word for eternal, according to the references on Biblehub are:
Strong’s Concordance
Original Word: αἰώνιος
aiónios: agelong, eternal
HELPS Word-studies
Cognate: 166 aiṓnios – properly, “age-like” (“like-an-age”), i.e. an “age-characteristic” (the quality describing a particular age; (figuratively) the unique quality (reality) of God’s life at work in the believer.
NAS Exhaustive Concordance
Word Origin: from aión
To put it in as simplified of a manner as possible, the root word aion means “age” and aionios means age-like. This type of age isn’t defined except in what this adjective modifies. Applied to God it means eternal, but nothing else is eternal unless in God (i.e. eternal life, life that is only eternal inside of God). Applied to punishment, it takes on more of the meaning of “age-of” but not eternal. The corrective punishment will take as long as it takes, relevant to what is being corrected.
To sum up, “eternal punishment” in Matt 25:46, according to the original Greek, would mean more of an age of corrective action for the benefit of that person—but not eternal torment to appease God.