Steam controller plus 'sc-controller' for linux. It supports other controllers too. There may be an android fork out there.

I also use it for most steam games, as I abhor steam input. I always launch steam with --nojoy.

I use RetroArch ~~btw~~ on my tablet with a cheap Bluetooth gamepad, and have L3+R3 (pressing both sticks) configured to bring up the menu where I can save/load states, take screenshots, etc.

RetroArch also allows you to map actions like fast forward or slowmo to gamepad buttons, and make it so you have to hold a specific button to activate hotkeys.

My emulator handheld used combos to handle that. Holding select and pressing shoulder buttons would load or save the state for example

Steam Input baybeeee!
Setup a virtual menu and then you can have as many shortcuts as you want on the touchpad.

That being said, if the games you are playing can be emulated in RetroArch, that would be the best option.

If I am able to, I go in and re-map the buttons (either this is done in game or in your emulator). Sometimes you gotta play the game a bit, see what the imputs "should" be and then go in and set them to match on your controller. So if melee is E, I'll bind it to B. If shoot is left click, I'll bind it to RT. It's kinda tedious sometimes but it's step I'm willing to take (where I'm able to).

This video is about pokemon fan games, BUT, at the end of the video he shows about setting up the buttons game by game, as an example for you.

I play at my desk and use both keyboard and controller.

If I wasn't at my desk, I'd just not use those functions. But you might also be able to bind them to controller buttons or combos.