I know it’s a long time, and maybe the topic is dead, but I managed to calibrate my monitor in Linux, although it was not easy and, honestly, the situation is quite sad.
So…
-
The “calibrate display” of Gnome is broken: it is known (see for example Draft: color: Fix gtk4 migration (!1501) · Merge requests · GNOME / Settings · GitLab and the related bugs) but it seems that really too few people care.
-
DisplayCal works, but (at least if you have a SpyderX like me — you know, black Friday) it works only if you have exactly version 2.3.0 of ArgyllCMS, because previous and newer versions have a bug Error – ‘Instrument Access Failed' for LCD White LED Mode | DisplayCAL. Fortunately, the FlatPack version has the correct one

-
It’s not immediate, but you have to choose the following options:

…and then follow the instructions. I managed to calibrate my old LG IPS display very near to my new BenQ (which come with a ΔE<3 certificate), so I’m happy now.
When importing the ICC profile, you have to convince Gnome to see it (restarting GNOME shell or something like that, I am not sure).
But the situation is not really a happy one. I was almost thinking of calibrating the monitor connecting it to a Windows machine and then exporting the ICC…
