Dream Pillager, after damaging an opponent, allows you to exile that many cards from the top of your library and cast any until end of turn that were exiled this way. Does this mean I may cast ANY card that has EVER been exiled this way since the beginning of the game?
No, you can't cast any card at all that's in exile that way. You can only cast cards that were exiled by Dream Pillager this turn, and only until the end of the turn.
Whenever Dream Pillager deals combat damage to a player, exile that many cards from the top of your library. Until end of turn, you may cast nonland cards from among those exiled cards.
In making this change they were trying to make it extra clear you only get to cast that bunch of cards just exiled, only this turn.
Compared it to the -X ability on Ashiok, this lets you cast anything castable that was exiled this way this turn until the end of turn, but you have to pay the right amount of mana and correct colours (there are cards that will allow you to pay any mana as the mana for it like Ghonti)
It says "Until end of turn, you may cast nonland cards from among those exiled cards."
This is implying that you can only cast the nonland cards that you exiled during that turn.