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.
They're definitely doing screen level analysis.
I work for a company that does some work on Internet advertising and one of the main issues that came up when we discussed supporting smart TV platforms was how we could protect our proprietary advertising audience data while still showing ads on these devices. Knowing what ads we show the user tells them what the user is interested in, which is valuable information for our competitors.
Unfortunately, we were not able to solve that problem, and instead to just use lower fidelity user models for advertising on smart TVs. That makes smart TV ads less valuable, but allows us to keep our competitive advantage on desktop and mobile.