Something with an in game timer or something so I can just play casually and post a screenshot of my times

Hey @Faulheit, join the mobile speedrunning discord!
https://discord.gg/bpY8zeB

We have speedrunning resources, competitions, and a ton of awesome games to play.
In resources, you'll find links to the Floating Speedrun Timer, made by one of our members for Android.

We also have resources for recording your screen. Since its pretty easy, most of us require full video with audio for verification.
You can also look here: Speedrun.com's mobile game list: https://tinyurl.com/ycqtss39