The game is NOT using/applying Xbox, Playstation or PC HDR Calibration app settings.
The game has a mixed HDR implementation as even if doesn't support system-level HDR calibration it does provide different in-game HDR controls including Peak Luminance (in nits) which can precisely go up to 4.000 nits...but like recent AC entries like Valhalla, it suffers from black level raise with default settings.
Let's see how improve it as much as possible!
If you have an LG OLED and:
> you're using Dynamic Tone Mapping or Dynamic Contrast:
Set Maximum Luminance slider to: 4.000 (nits)
> you're using HGIG:
Set Maximum Luminance slider to: 800 (nits) or 1.000 (for G2/C4) or 1.500 (for G3/G4).
If you don't have an LG OLED and:
> you don't have an HGIG option:
Set Maximum Luminance slider to: 1.000 (nits)
> you're using HGIG:
Set Maximum Luminance slider to the corresponding real Peak HDR Luminance of your TV in "nits"
In all cases decrease the Exposure slider to -0.3 in order to mitigate (but still not totally fix) the black level raise without losing Peak Luminance or average picture brightness.
BONUS:
On Consoles: use the "Balanced" (locked 40fps) performance mode if you have a 120hz TV for the best, well, balance between graphics/picture quality and performance. If you have a 60hz-only TV, use the "Quality" (30fps) mode instead as the "Performance" (60fps) mode has too much graphics downgrades in my opinion
Disable Chromatic Aberration: to improve picture clarity on all platforms