Pandemic Legacy is probably the best known, and I think there's a version of Gloomhaven that is massive, but also single-play.

Risk Legacy is another fun one, although it also suffers from the same "permanent changes" issue (feature?) described above.

You say "suffers from" as if it is not the core intended feature of the game. It's the same way ice cream suffers from being delicious, or baseballs suffer from being hard.

Here's the wiki: https://en.m.wikipedia.org/wiki/Legacy_game