Everything I write here may be entirely wrong, as ever since I delved into color management I forget even my own name, but as far as I know it’s correct.
What “color managed” here means is that the monitor profile is made available to programs which know how to use it (IIRC Windows uses an environment variable for that), and that the gamma calibration curves (if the ICC profile has them) are loaded into the VCGT (video card’s gamma table). Loading them affects everything you see on screen, everything changes, so you might be mistaken into thinking that everything is now color-managed, but that is not the case! The gamma curves get you only part of the way there.
Calibrated != profiled, two different things. Calibrate = tweak the knobs or press the buttons to get things (white point, tone curve, color balance) into the right ballpark, and optionally conjure simple gamma curves (1D LUT) which can but don’t have to be stored in an ICC file, which are to be loaded into the graphics card’s gamma table and therefore affect everything. Profile = feed the monitor a reference color, measure the result, document the difference, and store a matrix or LUT in an ICC file to correct for that. Color-managed programs can use the matrix or LUT from an ICC file to correct the colors.
As you see, the ICC file can contain multiple things, some of which (the calibration curves which get loaded into the VCGT) affect everything you see on screen, and others (matrix/LUT profile) which do not, and instead must be handled on a program-by-program basis.
If at the time the ICC profile was created there was a non-linear curve in the VCGT, then the same curve must be loaded into the VCGT AND the program in question must use the matrix/LUT profile for colors on screen to be correct. Using the calibration curves alone, or using the profile alone, will not result in correct colors.
This seems to be where you’re getting stubbornly confused. Just because an ICC profile is “loaded” in a color management system (Windows Control Panel, colord, DisplayCAL, etc.) does not mean you now have correct color everywhere. All that happens when you load this profile in a CMS is that the calibration curves are loaded into your VCGT (and so all colors on screen change, but are not correct yet), and some sort of standardized pointer is set (_ICC_PROFILE
X11 atom, environment variable, etc.) which allows color-aware programs (RawTherapee, darktable, GIMP, etc.) to find the ICC file and to use it.
RawTherapee falls back to sRGB when using “Monitor profile: None”.
Get an ICC profile with inverted colors, such as this one: cms/bgr-test.icc at master · haasn/cms · GitHub
This profile swaps the red and blue channels, so it will be immediately clear whether it’s being used or not. It has no VCGT calibration curves (i.e. linear).
Apply it the same way you should apply your monitor profile, and you will see just how color-managed your system is.