Here is the Greek word in question:

From the same as Strong’s G104; properly an age; by extension perpetuity (also past); by implication the world; specifically (Jewish) a Messianic period (present or future)

Both aion/eon and the Hebrew equivalent can mean either a long definite period or an indefinite one. When referring to or applied to God, they mean forever or everlasting or, as we would say, eternal. In most opinions, aion is used in the Jewish tradition, in the same manner that they used their own Hebrew word. The thinking did not change. Only the language changed.

I see a contrast is some verses. Aionian judgment is not eternal but aionian life from God is eternal. This is a logical presentation of an idea, and was common in the time of Jesus.

Also, there is a sense where God’s judgment is eternal. He judged sin and we are now judged righteous. For all time.

There is a lot of buzz these days about how eternal doesn’t mean eternal and it’s a mistranslation  But these words indisputably do mean everlasting/eternal. And they also mean a period of time, like an age. It’s not either/or. It’s both. One meaning applies God, and one to mortal men. Context is everything.

Is God going to punish people forever if they are sinners? No. More on that in another place.  And if you do not believe there is a hell, as a place for anything other than laying a corpse, then all this carrying on about whether or not aion means eternity, is pointless.

It’s hard to find good treatment of some of these words. The linked page does it well. I don’t endorse all the teaching on that site, but I’ve learned that truth is hidden in many places.