For the calibration, please change your Reference Mode on your Liquid Retina XDR Display to Apple Display (P3-600 nits). Here is a link to an article from Apple on the Reference Modes: https://support.apple.com/en-us/HT210435

When you calibrate, you get an ICC ColorSync profile, as expected. This profile is in effect “on top” of whatever the current Apple preset for the display is set to.

Because Apple has hidden the normal “MacOS System Preferences” ability to switch between ICC profiles for the internal display of the 14“ & 16" MacBook Pro 2023 / 2022 / 2021 with the Liquid Retina XDR Display, which use their “preset” system, the most convenient way to switch profiles is to use the SpyderUtility’s “Profile Management” feature (only Spyder X2 Ultra & Spyder X2 Elite / Spyder X Pro & Spyder X Elite) to do that instead. To switch back to the default Apple profile for the display, then you can choose “Color LCD” in the list.

The Apple’s ColorSync Utility application is another way to switch ICC profiles, but it’s much more technical and user unfriendly.