One big thing, this all assumes your TV has HDR support, without knowing the model of your TV, I'm not sure this applies.
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Put the Default setting in 4k, any version, This will just apply to your menus and screen saver.
here's the important part, turn on match rate and range, That will cause the appleTV to switch it's output to match what you're playing, If you don't have that turned on, it will modify the image to fit in what you have set for default. When it modifies what you're watching, it does an OK job, but can lead to less than desirable results.
One small note, with turning on rate/range matching, your TV will blackout for a second or 2 anytime the aTV changes it's output. So anytime you start or stop a video playing, Or also anytime the screen saver starts or stops. But you'll get the best image for what you're watching, so it's worth the trade off.
I leave mine in 4k SDR, it's way too bright for me in either of the HDR versions.
Also on your TV, there might be a setting for HDMI deep color, or something similar, make sure it's enabled for the port the aTV is plugged into. I had been playing around with something, and turned it off, and forgot about it. My TV has been dim recently and couldn't figure out why, then I saw that it was off, and re-enabled and my picture is much better now.
you also need a decent quality HDMI cable. It doesn't need to be $100+ and made with gold extracted from king tut's mask , but don't get the $1.99 bargin basement cable either.
If you're doing HDR, you need a cable that says HDMI 2.0 or 2.1 on it.
It should be around $25 for a 5ft cable