I don't have any 8k ProRes RAW but I have lots of 6k ProRes RAW from our DJI Ronin 4D and also 8k RED RAW from our V-Raptor.
I tried the 6k ProRes RAW in a 6k and 4k timeline, exported as 6k and 4k from the 6k TL using H.264 and ProRes 422, also the 8K R3D in a 8k TL and 4k TL, exported as 8k and 4k PR422 and H.264 from the 8k TL and 4k from 4k TL.
I viewed it on a calibrated 5k Apple Studio monitor. I couldn't see much difference in any of the permutations.
If you are viewing 8k on a 5k or 6k XDR monitor vs 4k on those same monitors, in theory the 4k should be less sharp -- it has 1/4 of the pixels of the 8k frame. If you are viewing it on an HD monitor, iPad, etc. I'm not sure you could see the difference.
If the final product will be uploaded and re-encoded for streaming, I tend to doubt you could see a difference during playback.
However I remember years ago there were some issues with FCP whereby 4k downscaled to 1080p seemed to be a bit too soft. I don't remember if that was resolved or defined as expected behavior.
As Ben said, anytime you rescale there will be scaling losses. That is why in Photoshop there are various resampling and scaling options (see attached). There is no single best way to rescale an image -- each algorithm has various tradeoffs.
I vaguely recollect some NLEs automatically add sharpening when rescaling, and FCP does not.
I suggest in FCP, duplicate the timeline, then in that timeline, remove all the effects with Edit>Remove Effects. Pick a frame and put a marker on it. Use the R key to draw about 2 frames, then export that as 4k H.264. Then do that in an 8k timeline with the ProRes RAW material, mark the same frame with the M key, use R to draw about 2 frames on the timeline and export that as 8k H.264. Examine those in Quick Look or Quicktime Player and see if there is any visible difference.