Any handheld consoles with parental controls? Mainly looking for timed sessions

Keep the batteries at or below 20%

It seems like Family Link on Android might be what you are looking for

https://www.techadvisor.com/article/726031/how-to-set-up-android-parental-controls-to-limit-screen-time.html

I think devices that use something like Emulation Station can only limit certain games and menu options but that still leave devices like the Retroid Pocket 3+. Anything that runs PC games should have it’s own suite of parental features or work arounds.

iPhones and iPads are not technically consoles but they do have very robust parental controls.