My TV only allows picture size adjustments in 1080p mode. In 4K mode, the 'stretch' option is greyed out. So when I want a full-screen picture of SD content, I set the ATV to output in 1080p so that option is no longer greyed out and I can resize my TV's picture. If I set the ATV to 4K, I cannot adjust the TV picture size. So I only set my ATV to 4K to watch native wide-screen content. I don't want to get into a debate over why black bars exist, I just hate seeing what appears to be a 25" postage stamp in the middle of my 65" TV when watching content that's stuck in 4:3.
I think what my TV is actually doing is showing at times what quality of picture is coming from the ATV itself. While the menus, etc are in HD, when an SD only show is being played, the TV is showing the resolution of that show. If I am watching something really old like Dennis the Menace from the 1950s, or the Andy Griffith Show, the TV's info menu shows 480p SD. It reverts back to whatever the ATV is set at when returning to the menus. I think this is a symptom of having the ATV connected to a surround sound receiver instead of direct to the TV.
That does not, however, resolve my issues with almost all content giving me a blurry rather low quality SD picture. Just watched some more DS9 just now, and while my TV shows 1080p HD as the resolution, the picture of the content still looks SD. The resolution seems to only apply to the menus, UI of the ATV itself, not the content.
So far, the only shows that are in HD quality are NCIS, Stargate: Atlantis, Stargate: Universe, ATV+ content, and Star Trek Enterprise. Those are the only shows in my library or on other services (Netflix, Hulu) that actually are outputting content in HD or higher. Only ATV+ content seems to scale to 4K, as my TV shows '2160p HDR10' as the source.
OK on my Mac the Farscape show has 'HD' showing on the title, right where the year is. But on my ATV it's definitely not in HD. It's 480p looking, with black bars on left and right if the ATV resolution is set to 4K SDR (which mean's it's NOT upscaling) and full-screen if set to 1080p SDR, but it's still not in HD either way. For some reason, my ATV is stuck in SD only mode despite any settings I make, except when streaming content that's in 4K, such as Apple TV+ content, or movies that are in UHD such as Intersteller and First Man. Shows such as Stargate: Atlantis are in HD proper, and look HD when streaming. But shows like Farscape, DS9, and Family Ties look completely awful on a 65" TV. It's like watching a TV with a dying CRT, very soft, very washed out color.