Games with roguelike metaprogression:

• Vampire Survivors: Practically an idle game. All you do in this is control your hero's movement around a sea of monsters and your hero automatically attacks them. Surprisingly fun and strategically deep. Battery killer
• Slay the Spire: card collecting strategy game
• Bloons TD 6 (requires Netflix): Pop Bloons with monkeys. Battery killer
• Into the Breach (requires Netflix): isometric strategy game from the same devs as FTL: Faster Than Light. Big emphasis on using near-perfect information to solve tactical fights like they are puzzles.

Puzzle games:

• Any of the variant Sudoku apps from "Studio Goya" on the Play store. These are the official apps of the Cracking the Cryptic YouTube channel. Handcrafted puzzles tend to have a very interesting solution path that requires you to develop logic skills.
• The Room. Play as Tommy Wiseau as he uncovers an Eldritch mystery by opening puzzle boxes. Very satisfying animations, neat story
• Cultist Simulator. Honestly idk what to call this one but "puzzle game" kind of fits. This is a really fun game but requires a while to get a hang of. In fact the fun of the game is learning the game mechanics, since nothing is explained except through cryptic hints and riddles. The writing is incredible but you will probably lose a lot as you get the hang of it.

Other stuff:

• Eternal Card Game: I'll be honest, I haven't played this in ages, but I remember it being a better MTG clone than MTG arena. The mechanics are almost the exact same feeling as MTG, but more adapted to the digital medium. Has some pay-to-win mechanics and microtransactions but honestly the pricing felt pretty fair to me and it's not super in-your-face with it.
• RCT Classic: Rollercoaster Tycoon 2 mobile port. It's not as good as OpenRCT, but it's still a lot of fun.
• OpenTTD: Transport tycoon deluxe mobile port.
• Papers Please: Glory to Arstotzka!
• Townscaper: not really a game as much as an arts and crafts kit. You get a tile-based map and wherever you click it fills in a tile. Depending on how you fill in those tiles, they look like different little buildings, gardens, etc. really cute game with no stakes.
• Mindustry: minimalist Factorio clone. Controls can be challenging on mobile but it's still fun