IINE Retro Pocket Game Controller with Hall Effect Joysticks, Switch 1 & 2 Compatible, Wireless Gamepad for Steam Deck, PC, Android, iOS, Customizable D-Pad, Vibration & Motion Control (Purple)

If you want cheap pocketable controllers: AceGamer Wireless Pocket Controller IINE Retro Pocket Game Controller I used to like the 8bitdo lite 1, but having no control stick is actually a bummer for a lot of games. And the 8bitdo lite 2 control sticks just make it not pocketable.

For Bluetooth, I use this 8bitdo controller I can also vouch for IINE Pocket Controller NS. If you don't put on the included silicone caps, the most sticking out part would be a d-pad. Very easy to slide in and out of pocket or bag,