Josh Centers, TidBITS:

tvOS 14.5 has introduced a new feature, called Color Balance, that can automate the process of correcting the colors on your Apple TV.

Note that this changes the video that your Apple TV generates, does not change your TV’s own settings.

The feature is available on all tvOS-compatible Apple TV models: the Apple TV HD, first-generation Apple TV 4K, and the upcoming second-generation Apple TV 4K. However, you need an iPhone that supports Face ID.

And, interestingly:

To get started, update your Apple TV and iPhone to tvOS 14.5 and iOS 14.5, respectively. Color Balance calibration will fail midway if you have HDR enabled, so you’ll want to disable HDR on your Apple TV in Settings > Video and Audio > Format.

Really well done walkthrough, worth exploring.