[Feature request]: Add the option to hide the touchscreen overlay with a button / after a few seconds / only when a controller is detected

Is your feature request related to a problem? Please describe.

Currently, the only way to toggle the touchscreen overlay is to exit the game, go to settings, then toggle the overlay. This makes the screen needlessly cluttered when playing with a physical controller, as most of the time the buttons on screen are redundant, but sometimes they are required (for example for buttons not on the controller such as the home button).

Describe the solution you'd like

There are several options that could be added to the application:

• Hide the touchscreen overlay by touching a "hide" button, and display it again by touching the button again.
• Hide the touchscreen overlay if the user has not touched the screen after a few seconds. Steam Remote Play includes this option, which defaults to about 5 seconds.
• Hide the touchscreen overlay in case that a physical controller is being used.

Describe alternatives you've considered

So far, the only workaround that the application shows is to toggle the overlay BEFORE starting the game.

Screenshots

No response

The issue names no files, tests, or entry points. Start by locating the touchscreen overlay and its existing settings toggle, then inspect the relevant touch and controller-input handling; done means implementing and validating a clear way to hide and restore the overlay under an agreed option.