MLS

Yeah, you're right. I just verified the behavior by dragging the AP window from monitor #1 to monitor #2, and I can see the colors of the document change as soon as I stop dragging the window (thus placing the window on monitor #2), which I take to mean that AP is now taking monitor #2's ICC profile into account. Sorry for the false alarm, then. My bad.

It also seems... let's say counterintuitive that the color profile of the monitor that the Affinity Photo app gets launched on should determine the color management inside Affinity Photo for the duration that it is open. Doesn't that mean that if I move the Affinity Photo application window to another monitor, the colors there will always be wrong (since that monitor will be using a different, calibrated profile than the first monitor)? I was wrong about this bit. See below.

To add one more example of the issue, here's what it looks like on my screen. The file being shown is the first Google image search result for "black and white gradient", there's nothing special about it and any other image from that search will demonstrate the issue as well. To the left is Affinity Photo 1.9.1, to the right is the Windows Photos app (it doesn't matter that it's the Photos app — every other image viewer installed on my system other than Affinity Photo will display the image like this). You should be able to see that there is a difference in color(!) tint for the grayscale(!) gradient across apps. Affinity Photo's Color settings are unchanged from their defaults. As @Dennis Schmitz has already said, the only way to get Affinity Photo to match the other apps seems to be to set the color management profile used by Windows to sRGB IEC61966-2.1 (which amounts to not using a calibrated profile for that monitor) and then relaunching Affinity Photo. I really don't want to do that every time I open Affinity Photo, not in the least because it of course affects all other apps which I might be looking at on that monitor as well.