Pokemon Go (Android/iOS)
I don't think I need to introduce this one, least of all on a Pokemon forum. I grabbed it during its heyday in 2016 when my phone was melting trying to run it, played it while it was fun, and put it back down. Then when a friend of mind asked me to check it out again in 2019, I had a better phone and found that the game had expanded greatly since I saw it last and was generally more accessible to the casual player. Since then, I've kept it up and met really cool people in my community who play the game. Also with the remote raid system, I've been able to do stuff with people in the CAP community.
That being said,
Pokemon Go is definitely a game that requires a guide in order for you to have fun with it (IMO). E.g. fast catch is an essential skill, and I don't think I would have stuck with the game had I not learned about it early on.
Simon Tatham's Puzzles (Android/iOS)
Honestly, this post was made so I could plug this app. :P This is an old, old set of 38/39 puzzle games that has been ported to every platform out there. It's lightweight, completely offline, lacks ads and microtransactions, and is designed to be completely fair. (E.g. their version of Minesweeper ensures that the field is solvable.) I get bummed seeing games on the App Store/Play Store that are simply one of the games in this set with a fresh coat of paint and riddled with ads and microtransactions.
Assorted indie puzzle games
These are all indie games centered on a unique gameplay mechanic which you can complete in a single sitting.
The phone ports of beloved DS classics
Also
Check out console emulators. The control scheme is a bit finicky on a touchscreen, but it's effectively access to an entire library of games from other platforms. They also fall into the category of games that are lightweight, ad-free, and no internet connection required.
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Since I got back into Pokemon Go, I haven't had time for any other phone games, but I wanted to share these ones anyway. :)