When I activate the Steam overlay within a game, input is still seen by the game (I tested mouse movement, mouse clicks, keyboard input, and gamepad input). It does however seem to prevent other input devices from sending input to the game (Thrustmaster HOTAS).

Steam:

• Proton Experimental (2021-08-29)
• Steam Input disabled

Tested games:

• Elite Dangerous (using a mix of mouse, keyboard, gamepad, Thrustmaster HOTAS)
• Horizon Zero Dawn seems to be blocked from the overlay using a gamepad but this game also forces Steam Input
• Grim Dawn (https://github.com/ValveSoftware/Proton/issues/5125#issuecomment-913305921)
• Other games not yet tested, most of which I play with gamepad only, thus the problem may not apply as I use the overlay with keyboard and mouse (see below, there won't be a conflict/race between game input and input for the overlay)

Tested devices:

• Mouse movement is seen by the game but it (probably the overlay) also seems to reset the mouse position as seen by the game to the screen center, but I am able to focus buttons below the overlay
• Mouse clicks get passed to the game, selecting unintended functions of the game in the background
• Keyboard presses seem to be seen but I only tested ESC which closed the overlay but also returned the game to the main menu
• Gamepad input can be used just as if the overlay wasn't there
• My HOTAS doesn't seem to pass through because I could no longer use it to navigate the in-game menus behind the overlay