What was the answer? I just got an iPhone 13 pro max. Video of tv is ok, but if I take a picture , it’s blue tinted.
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The Original Poster never came back to comment on my suggestions.
You have to realise that things have moved on apace since March 2020. The design of the camera system and the change from iOS 13.3.1 to iOS 15.5 means that some of my comments above no longer apply as they have been superseded. Some of the settings I referred to have gone.
It's easy to understand why a video would render a fairly accurate rendition, but a still photograph is a near instant action and colour accuracy is much harder to achieve. As blue is a dominant colour on home TVs, a tint is difficult to eradicate.
The only thing that might help is for you to experiment with "View Full HDR" turned ON and OFF to see if that helps.
This setting can be found in Settings > Photos > HDR.
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BTW, if you are looking to have your photographs go automatically to "My Photo Stream" and from there to appear automatically in the Photos app on your Mac/PC (if you have one); there are new settings that, for the moment anyway, need to be set.
Settings > Photos > Transfer To Mac or PC > Automatic (not Keep Originals)
AND
Settings > Camera > Formats > Most Compatible (not High Efficiency)
It didn't used to be necessary to change these, but a glitch in recent upgrades and updates means that, for the moment anyway, you need these settings.
I have an iPhone 13 Pro as well (not the max).
Please tell us if these comments help your situation.
Ian