On my Apple TV I can search for shows on HBO, Amazon, ESPN, etc. All of my recently watched shows, regardless of streaming service/channel, show up on the main "TV" page. I can use Siri to search across all services, e.g. if I ask Siri to play The Office it will find it on Peacock and play it directly from there.

The large exception here is Netflix, apparently they don't hook in to the Apple TV API like the rest of these apps do (I imagine it's the same on the Google TV).