I have the very same thing you have, and I have started seeing banner ads from Roku on my Apple TV! It appears in the form of a banner overlaying on top of my Apple TV content saying something on the lines of “more ways to watch this content”. I haven’t interacted with the banner yet and don’t know if it’s actually scanning the content to generate recommendations, but regardless I thought it was incredibly invasive of Roku to insert ads into a service it had absolutely nothing to do with.

This thread reminded me of the issue and I’m currently looking into how this can be disabled. Apparently there is a Roku setting that can disable these ad inserts — if that doesn’t work, off with Roku’s internet privilege. Apple TV’s UX is leagues better anyway.

Those sticks have probably as much processing power as whatever is inside modern smart TV's. It's still more than enough to modify HDMI output and add things that were not in the original source (like banner ads).

I don’t love the Apple TV (especially the remote), but every TV in the house has one connected. It makes watching TV tolerable. Not great, but at least tolerable