in PS, in color settings under Working Spaces, among the options for RBG, one is the monitor profile. This is the profile the system has announced to PS.
I don't believe that's correct. Your Working Space profile is just that. It shouldn't care what monitor profile the OS is using or if a monitor is even connected at all.
In my ancient Photoshop CS5 my working space is set to ProPhoto RGB regardless of which monitor cal profile is active. I don't know why yours changes, that seems bizarre.
Was this a fresh install of Win 11 and apps, or did you do an upgrade-in-place from Win 10? If the latter, I wonder if your Dell CM software got buggered up during the Win update. You could try un/reinstalling it.
I don't even have that Colour Management toggle in my Win 11 Settings (see screenshot).
I just finished building this PC to replace my old Win 10 PC and it has a fresh install of Win 11 Pro. Multiple monitors but at the moment I only set up colour management for the Eizo CS2740, using their Colour Navigator software. I haven't touched any colour-related settings in Win 11. When I change monitor cal profiles using either the monitor's buttons / on-screen display, or by using the menu in the Colour Navigator software, the active colour profile in Win 11 Settings changes automatically. So it appears Colour Navigator is doing what I paid it to do lol.
I haven't decided yet if I'll reinstall SpectraView for the old NEC PA271W monitor. But I expect it to behave similarly, like it did in Win 10.