Disable Screen Recording prompt from bluetooth game controller (maybe Big Sur only?)

I have an 8bitdo bluetooth controller that I use to play games on my Macbook with the latest Big Sur. I think since the upgrade to Big Sur, sometimes when I am using the controller Mac OS will break fullscreen to pop up a series of confirmations about whether I want to allow different apps that are currently running to record the screen. I have to click through each one to get back to my game. This happens whether I'm actually playing a game/have Steam open, or if I am just sitting on at the desktop. It happens when I have the controller connected to the Mac and press Select and Start at the same time, or sometimes Select and the Special/Meta button. It doesn't happen every time I press these combinations, I do have to press them multiple times to get the issue to repeat, but it happens very often. Is there any way to disable screen recording or this "shortcut" or whatever it is? I almost never want to record my screen, so turning off the feature would be fine if possible.