The biggest thing is that you won’t know how long you will be able to play it. At some point they’ll stop updating the app, a new Android version will be released that’s not compatible with the app, or they will take down the server that the app relies on etc. It could be years, a decade, but at some point it’ll be either really hard or impossible to play anymore.

Not sure if you’d consider them ‘retro’, but the Professor Layton ports are all excellent! I think each game is about $10 and the first 3 from the Nintendo DS are available. Works perfectly as they were designed for touch screens. Highly recommend!

Several Dragon Quest titles are available on Android. I believe DQ 1-3 are unique versions made for mobile. They are also available on Switch. DQ 4-6 were only ever released in NA on the DS and are damn near impossible to find now for a good price. But the mobile ports are based on this version and it’s probably the most accessible way to play those games. At least if you don’t speak Japanese.

If you’re talking about playing on tablet, it’s best to play the games through emulators or open source sourceports rather than paid store releases. As another comment mentions, you never know when the company that made the port will stop updating it for new OS versions.

ScummVM works well for playing old point and click adventure games on Android phones. More screen real estate on a tablet couldn’t hurt. Supports over 250 games. I’ve gotten tons of playtime out of it.

I regularly play turn based RPGs on my phone through Retroarch (and more recently Lemuroid which is the same core but minorly better UI).

I also use a handful of emulators and source ports with a controller mount to play more action-y games off my phone, but I don’t think that’s what you’re looking for with playing on a tablet.

For tablets, stuff I’m aware of but haven’t used myself: There’s android ports of OpenXcom, OpenTTD (I think), and Theme Hospital.

There’s also a pretty long list of source ports here, with the OS’s they support listed.

Edit: if you aren’t already playing old games through emulation, the world is your oyster.

I use launch box on android. Load my own roms.

Heroes of Might and Magic 3 (you need a gog.com version) together with the VCMI. If you like heroes 3, this is a great option. Some elements are rather small on my fairphone 4 phone.

I use an 8bitdo SN30 Pro + 8Bitdo Smartphone Clip together with emulators on my phone to enjoy Gameboy, SNES and PSX, I’ve also tried emulating some newer consoles but my phone is a bit weak for that.
There’s a ton of great controllers to turn your phone into a proper gaming device, I chose the 8Bitdo because I can also use it with my computer over Bluetooth.
But if that isn’t a consideration then I would probably go for one of those that has passthrough USB-C Charging so you can charge both controller and phone while playing.

Before I got the controller I mostly played Gameboy Pokemon games on my phone.

I still question myself why did not I try it before as it changed my quality of waiting on different places like public transport by large margin:

Try turn based games with Lemuroid (frontend for emulators on android). No gamepad required, always in your pocket, everything works out of the box.

I’m playing psp Valkyria Chronicles and it is great. Such games are perfect format for phone, as anything where reaction and precision is necessary needs gamepad. And you either need to own a retro dedicated handheld and take it with you, or (if you have one) take cumbersome Steamdeck like handheld, which is not feasible for 30 minutes ride.