To be clear, some ”smart” TVs include a technology called (if I remember correctly), ACR, Automatic Content Recognition, which literally watches the patterns on the “screen” from the incoming HDMI signal and tries to match that up against known content (for instance anything showing on cable tv right now), to figure out what you’re watching, so it can report that information back to headquarters, so the TV manufacturer can track and monetize you. This is reprehensible, regardless of whether or not they mention it on page 23 of the fine print, it’s basically spyware. Vizio got caught doing this quite some time ago, and as a result, they’re now required to include a toggle (buried) in their settings to turn it off. Not sure about the other manufacturers. It’s definitely worth looking through the TV’s menus.
If your smart TV is connected to the internet and hasn’t been specifically told to cease and desist, it may be reporting on your viewing habits/history, and the Apple TV in and of itself won’t fix that. If you hook up an ATV and disconnect your smart TV from the network, then you should be safe (although note that some smart TVs go so far as to look around for nearby/neighborhood open WiFi networks to use to report back to headquarters, so simply unplugging it may not be enough).
But the Apple TV won’t report on you, and will feed only HDMI signal content to the TV. The apps themselves, of course, know what you’re watching (i.e. the HBO app knows what you’re watching on HBO, the Disney+ app knows what you’re watching on Disney+, etc.)