Intel FCPX project colour grade doesn't match on Apple ARM / M1 Studio

I have several Intel and Apple Silicon Macs, have graded V-Log material on both, and have not seen what you describe. There is one specific case involving the FCP "Save Current Frame" function that behaves differently starting with Sonoma and Sequoia on Rec.709 content, but that is a MacOS problem, not FCP. And you are apparently talking about video, not an exported frame.

Even though you have the same physical monitor, are you using the same display profile? If not, that can make a significant difference in color or gamma. The display profile is seen in System Settings>Displays.

Since it's V-Log material, that would normally use the built-in camera LUT as seen in the Inspector's Info tab, General view. If on the Mac Pro, you used a custom LUT and the M1 the built-in LUT (or vice versa), that would make a difference.

Pick out a problem clip on your timeline, and examine if the V-Log LUT is applied (or the same custom LUT if you used that).

Are the problem clips all in a multicam or compound clip? If you also graded the original parent clips, it can be complex to figure out, because there are three locations to apply color: the parent clip, the multicam container, and the clip inside the multicam. If this is the case, examine what grading effects are applied at each level.

When originally grading, did you use the waveform or vector scope? If so do you remember any of those levels? The scopes obtain their signal in the video pipeline before some other attributes are applied (I think before the display profile). If the prior color state is available to inspect (say from the ProRes copy you made), it could be revealing to examine the same scene in the scopes between that and your current timeline.

If you shot a ColorChecker card that would be handy to examine. If not, I'd suggest doing that on the next project and taking a frame grab of the vector scope for reference.

I believe the few bits I converted to optimised/pro-res maintain their colour grade

I think you have the answer yourself. Please optimize.

How was it graded? With built-in color tools or 3rd party? Post screenshots comparing the two and the effects applied? You're sure that monitor calibration is correct? I recall discussions here about changes in recent MacOS.