The only real question is whether they're doing screen-level analysis or just relying on app telemetry

If I’m understanding you right, I’m confident it’s screen analysis. I have a Hisense Roku TV I exclusively use with an AppleTV. I get creepy intrusive popups telling me: “you could be watching this on other streaming providers!” all the time. So it “knows” what’s being displayed on the screen regardless of what app (or HDMI input) is being used.