Fair enough, hence why I mentioned the BT controller but OK so might want something more compact, say if you are walking around or in the subway for 1 stop.

That's not my situation so naively I'd suggest stuff like https://hexgl.bkcore.com/ or (and sadly I can't put my hand on it right now) those who rely on accelerometer, this way you don't even tap on your screen.

That being said I think there are also now Web based emulators that do have controller overlay. This way you use your entire screen real estate but also use the device it as a controller. There is no haptic feedback but works relatively well, I used that for WebXR on mobile.

Edit: it wasn't any of these but still gives the idea https://forums.libretro.com/t/rgpad-a-universal-gamepad-overlay/41134 https://github.com/ShawnHymel/phaser-plugin-virtual-gamepad/