[Windows] Can other processes read arbitrary data from inside a browser

This is Windows 10 specific. I was alarmed today when Nvidia GeForce turned off persistent screen recording (called ShadowPlay/Instant Replay) as soon as I accessed "netflix.com" on Firefox 96. They claim it is to deter users from screen-recording DRM protected content.

Besides the privacy concerns, I'm very curious to know how GeForce Experience process does that? Does it get assistance from Windows (PlayReady etc.), or can a process just do that. I'm looking for a technical explanation. How about some process reading how many times I visit my bank website per day? Where does it end?