tvOS (AppleTV 4K) does not have a user adjustable "Optimize Storage" setting as it only caches all content temporarily. All photo's are downloaded immediately in full quality when shown on screen. Video's too.
The issue is probably the encoding of the files. Photo's on AppleTV usually look fine when they are not shot with HDR on the iPhone. Most TV's use LCD panels and these inherently do not display HDR very well.
Same is with video, HDR just doesn't look great on LCD (TV, Mac's and PC's even worse). I've got some indoor shots that look fine on the iPhone 13 OLED display, but show very blocky and (MPEG) blurry on our LCD TV. The conversion from HEVC, ITU-T H.265 to Dolby Vision on our ATV 4K (2017 model) just looks horrible.
Maybe the results are different on newer ATV 4K models that have (hardware) H.265 support. I don't own the newest model at this moment.
For now I've turned off HDR on video recording on our iPhones. For photo's I've kept HDR turned on as they look good enough on a Panasonic 4K TV with Dolby Vision. Same photo's look horrible on a Samsung 4K... but that seems to be "the normal" on Samsung.