@Georgy
X11 supports CMS more or less well. Even I was able to profile the
monitor and install it with colord. It's not full support like Windows
or Apple has, but it's doable.
For Wayland the big problem, why they didn't want to make a CMS, is
its being decentralized, a protocol to which various software could
interact by bringing their own version of CMS. The trouble is that a
CMS must be centralized by definition, if everyone fakes their own
implementation goodbye std.
On Wayland, good programmers but bad color scientists, they didn't
even know how to start. Then Valve created The Gamescope to be able to
play games in HDR, and Wayland started from that to implement its CMS.
The result is not a real CMS but just something for video games and
movies. True, lately they seem to have figured out the problem and one
can hope that they will be able to solve it.

For the time being, the main developer said:...
The color-management Wayland extension is enough for entertainment
purposes like games and movies. However, it is not enough for
professional color management needs including photo editing and print
preview. The major missing piece is the ability to measure the display
response. Every monitor is unique, and measuring is the only way to
achieve reliably repeatable and accurate display behavior.
...

Introduction to CMS in Wayland by the lead developer:
https://www.collabora.com/news-and-blog/news-and-events/12-years-of-incubating-wayland-color-management.html

A summary by Paalanem of everything that happened in the 12 years of
development:
https://gitlab.freedesktop.org/pq/color-and-hdr

Old discussion on monitor profiling (in the thread, user Graeme Gill
is ArgylCMS's developer):
https://gitlab.freedesktop.org/pq/color-and-hdr/-/issues/27

Wayland CMS implementation in Gnome:
https://gitlab.gnome.org/GNOME/mutter/-/merge_requests/4291


A theoretical question: can CinGG be adapted to work in Wayland or is
it impossible? Has XWayland limitation?