Yet this was released under their term and not previous presidential terms

> previous presidential terms

Term, not plural. There was one (1) interceding administration following Epstein's death.

Trump promised that the Epstein files would be released if he was reelected, and then withheld files. Congress passed a bill remediating this, hence the newer tranche of files: https://en.wikipedia.org/wiki/Epstein_Files_Transparency_Act

Im not too deep into USA politics and have very very bad memory so i dont remember how it went down. The Wikipedia article you linked says it was signed by trump.

>and then withheld files.

So did he sign that willingly in the end? Did he have to sign it? Did he cave because he said publicly he would?

A super majority in Congress voted for the files to be the released, which is enough to override a veto, so he had to sign it to save face.