The game is NOT using/applying Xbox or PC HDR Calibration app settings.
The game has a decent HDR implementation as Peak HDR Luminance seems fixed to 1.000 nits and there's no way to change it in-game.
Luckily though, black levels are almost perfect with it.
The only available in-game slider is related to a generic "Gamma" setting
which you can set to Gamma 2.2 for a more accurate picture.
Then in the end, if you have an LG G2/C4 or a 1.000 nits Peak HDR TV, use HGIG
For all the others TVs you can try enabling Dynamic Tone Mapping
BONUS:
The game was intended to use a "stop-motion" effect which will purposely lower framerate in character animations but not for the entire game. So for example on Xbox the game will always run at 60fps and input latency will be good but characters' lips or movements will purposely move to 15fps to give the impression to be in stop-motion using real puppets, so as a creative choice. You can disable stop motion during gameplay from the game settings but I do recommend not doing so to respect the game's unique artistic vision
On PC version only: try my Optimization Mod to improve performance and picture quality, remove stutters, reduce latency, all with no visual loss ;)
Enjoy ;)
-P