Lichess

Aurora Store, a way to access Google Play’s Store (explanation likely slightly wrong), has a filter for “free” and “advertisement free”. Do a search for “open source games”, add those filters and then check the web pages for any games that look interesting. Similar filters do not appear in the official Google Play Store.

Sometimes it’s fun to smash some AI in the game Feudal Tactics (or get wiped out). Not a thorough game, but it’s surprisingly repeatable if you’ll get along with its vibe.

And generally F-Droid.