Most mobile games through the app store are ad filled garbage. The two big exceptions ive found are Game Pass on mobile, and Netflix games. Netflix games are basically the mobile games with all the bullshit taken out.
Slay the Spire and Monster Train have been my favorites lately
I've been hooked on Knighthood recently. It's a fun little RPG with simple mechanics. It is also in portrait mode so it's perfect for one handed play.
Prior to that, I had primarily been playing Archero which is another very fun portrait RPG.
Although I primarily play it on PC, I love that I can also play Albion Online on mobile, especially for some of the mundane farming and auction house tasks.
Other than that, I mostly stick to puzzle games like Woodoku, Wordscapes, Tents & Trees, and Grids of Thermometer.
Pokémon Go by Niantic, provided you live in a high population area (or an area with plenty of Points of Interest, or POIs). The premise is you walk around outside and catch Pokémon - the game uses GPS (think like walking around with Google Maps open).
I recommend it, but the player motivation is probably as low as it has been due to Niantics decisions to walk back COVID decisions, as well as the general state of the game (bugs etc.), but it's fine to motivate you to take a daily walk for sure, or just something to do on a commute if you are sat on a bus for example.
Ingress which is the first game Niantic made, and laid the foundations for Pokémon Go regarding the map (the games generally share the same POIs). It's more competitive as there are two teams and you fight for control over the POIs whereas in Pokémon Go the POIs are generally places to restock items. It uses GPS like Pokémon Go.
Again I recommend this, if not to at least check out for an hour. The game doesn't hold your hand as much so it's best to join a nearby community.
Another Ingress agent here. I've been playing on and off for 9 years, and it still keeps me interested. Personally, I prefer playing on my own, rather than co-operating on big ops, but since I live in a rural area that's kind of the default anyway. I don't drive, but I can reach 4 or 5 small towns by ebike which have a good bunch of portals, and have a couch portal (a POI across the road, within 40m) so I can keep stocked up on items between trips outside. I've walked/biked over 4,500 km while playing.
(While typing this I've realised you probably mean "played on a mobile device" rather than "games that keep you mobile", but there we go.)