It appears this behavior was reported in the Apple MacOS forum on Sept. 23, 2024 and possibly reported via the Apple feedback system. It's obviously not fixed, possibly due to a poorly-described scenario: macOS Sequoia Bug - Preview misinterprets… - Apple Community
Anybody who wants can report this (again) via the Apple feedback web page: Feedback - macOS - Apple
However, testing on multiple machines shows the behavior is quirky, has state dependencies and may involve both video and still-image metadata. There are several software layers below what you visibly perceive that involve how ColorSync works with embedded color profiles and display profiles on various hardware and MacOS versions.
I and a colleague who is an expert on MacOS ColorSync recently spent several hours on a Zoom conference studying this issue. During that conference, the problem vanished on one of my Macs, then later reappeared. We intend to pursue this next week.
The problem is apparently related to the embedded color profile 'Rec. ITU-R BT.709-5' used by FCP when doing Save Current Frame from a Rec.709 project. By contrast, Resolve (despite exporting from a Rec.709 timeline) uses the embedded profile 'SRGB IEC61966-2.1'. This doesn't mean FCP's use of that particular BT.709-5 profile is wrong but more likely, how ColorSync handles it is wrong. So it's likely not a bug with Preview or Quicklook or FCP but a deeper MacOS problem.
As described above, the frame exported from FCP can be patched using the command-line tool ImageMagick to have a regular ICC-type Rec.709 profile, which seems to avoid the problem.
It's possible to automate that via a MacOS shortcut, whereby it monitors an output folder for .jpeg files from FCP, then automatically patches them. I don't have time right now to produce that, but it should be straightforward.
Also as described above, it's possible to take a full-screen capture of the FCP viewer so that it's dimensionally perfect, and without drawing a capture box by hand. That also works around the problem. However, when going to full screen, FCP playback immediately starts from the current frame.
To prevent this, you can do the command sequence I, <right arrow>, O,/ (I key, right arrow key to advance on frame, O key to mark end of 1-frame range, forward slash key to loop on that one frame, then SHIFT+CMD+F for stationary full-screen viewer on that frame, and SHIFT+CMD+3 to capture that). That can all be automated via a MacOS shortcut, at least to some degree. I have a provisional Shortcut + AppleScript that does that, but I want to test the usage on various machines before I post it.