X is color-managed to the same degree that it is in Wayland. That is, all buffers are sRGB, and the application needs to convert output buffers in sRGB format. Chrome certainly takes great care to do color management of the content displayed in the window, but again, it is limited to sRGB output. This is the same in Wayland and X.
Color management needs improvement across the kernel & drivers, the compositors, and the applications. For more details on implementing color management, see Henry Wentland's 2022 XDC talk about implementing HDR (a feature that requires robust color management up and down the stack). You might notice that it primarily focuses on Wayland.
There's a lot of talk about HDR and Chrome here. I'm interested in neither but me and other professionals (in photography and graphic design) that do color critical work need to be able to create color profiles with spectrophotometer hardware and https://displaycal.net/ and use those profiles. It's a well known fact that this is currently impossible with Wayland but possible in X. Developers of darktable, Rawtherapee, Krita and other open source applications hang out out on pixls.us. Here's a thread:
Okay, my situation is that I have a monitor that displays a larger than RGB color gamut. When I set an ICC profile for my monitor in GNOME, and go to a page that should be in an sRGB color gamut in Chrome in X, it displays it as it should look. In Wayland, it displays it in my monitor's native (wider than sRGB) gamut.
Color management needs improvement across the kernel & drivers, the compositors, and the applications. For more details on implementing color management, see Henry Wentland's 2022 XDC talk about implementing HDR (a feature that requires robust color management up and down the stack). You might notice that it primarily focuses on Wayland.
[0] https://www.youtube.com/watch?v=nDnbWaIMJJA