Pokemon Showdown also works great in a mobile browser, it's a free, open source, highly popular PVP battle simulator and team builder: https://pokemonshowdown.com/
There's a handful of games that are good on mobile - Bloons Tower Defense 6 comes to mind (does have micro transactions but they can be easily avoided to be honest)
But the fact that you can get Retro
Arch and play any game from like the PS2 and older is amazing
If you get a controller like the Razer Kishi for example you can have a Switch-like experience
I've yet to try it, but I was gonna play Ocarina of Time and Majoras Mask using my phone and Retro Arch