Some paid games use drm which needs gplay services to function.

MicroG is what probably is making it work for you. However not everyone uses microG.

Check out Mull or Mulch. Mull is a more private Firefox and Mulch is a more private Chrome. They are made by the DivestOS team, they also make DivestOS which is a lot more private Android version that supports a huge number of phones. That’s how I’m also runing the latest version of Android 13 with the latest security updates on a phone from 2019. And there are much older devices supported.

I wouldn’t recommend using Yandex, due to it’s connections with the Russian government. You should check out privacyguides.org they have a lot of cool info about privacy respecting tools. However I also don’t recommend anything Brave. The company was founded by a homophobe who was previously in charge of Mozilla, but left, because of community pressure.