VCMI - it’s re-written from scratch, open source, multiplatform Heroes 3 engine with many improvements and mods manager. It requires some files from the original game though.
The modding scene is (or, well, was) pretty active though, if you’re into that. There are still official te4 forums, but most folks hang out in the discord (yeah, I know.) including a couple old head modders that are pretty familiar with the codebase if you’re trying to do something exceptionally interesting with it.
From a quick video I saw, they seem similar indeed, but I haven’t played Thrive enough. I have only made it to a single-cell prokaryotic organism, lol (which is basically very close to the beginning of the game).
I played this in high school circa 2013. There was a server up 24/7 that hosted an infinite loop of the Venice map that always had the highest server pop. You’d occasionally find other servers going, or be able to host your own and get randoms, but more often than not, I played a TON of Venice for about a year. Good times.
No variant rules unfortunately according to the Fdroid. You should check out the sudoku games from Cracking The Cryptic on the Google Play store if you want that. They aren’t FOSS but they have hundreds of handcrafted puzzles for a few bucks.