[Edit: while I was writing this long-winded response, @vazandrew offered good advice to try first! Could be the YouTube app has simply gotten confused :-)].
This could be a mismatch between the video settings on your TV and the ATV4K. Perhaps you turned on the ATV4K's video settings for Match Content, and you're encountering frequent changes in content's frame rates and color range while watching streaming live channels (old/new programs, commercials, etc.). The ATV HD is likely converting all content to 1080p.
My advice is to set your TV's video settings to factory defaults, then enable any advanced video features (HDR, Dolby Vision, enhanced HDMI, HDMI CEC, etc.) for the HDMI port that the ATV4K is connected to. Note that some TVs have only one or two HDMI ports that support the advanced features that the ATV4K is capable of (HDR10, Dolby Vision; Atmos, etc.). Next, go into the ATV4K's Settings > Video and Audio and do a Reset Video Settings. The ATV4K will handshake with the TV and land on the TV's preferred video format (4K SDR or HDR). Then, enable and verify any advanced features or enhanced chroma values that your TV and the connecting HDMI cable can support. Try the iPhone color calibration process to see if you like it and maybe choose your favorite video settings on the TV side.
My advice is to leave the ATV4K's Match Content settings at default (off) and see if the YouTubeTV issues persist when the ATV4K tries to convert all content to match your TV's best video mode. My experience is that it does a pretty good job of video processing. If you see issues, then try making adjustments to address them.