When you moved apps to your new Mac it may have copied over AU cache files from a prior MacOS version. If so that's an example of why it's best to perform a clean install of apps and plugins from scratch on a new machine.
Use Terminal’s auval -a | grep -i "LowShelfFilter\|MultibandCompressor" to confirm exactly where the system is loading these from.
On my machine running FCP 11.0, Compressor 4.9 and MacOS 15.2, it gives this output. If yours does not say this, post what it returns:
aufx lshf appl - Apple: AULowShelfFilter
aufx mcmp appl - Apple: AUMultibandCompressor
In Finder go to ~/Library/Caches/AudioUnitCache/ and remove any *.cache files inside.
Reboot your Mac, which restarts the audio daemon process.
Launch FCP and Compressor. On the first startup after clearing caches, the system re-validates the Audio Units. Check if the error persists.
If it still happens, use these terminal commands to individually validate those two MacOS AU plugins. Save the output and inspect for any validation or other errors:
auval -v aufx lshf appl
auval -v aufx mcmp appl
However, the above MacOS commands are generic. The FCP/Compressor validation checks run by the "Flexo" private framework are much more detailed. That could potentially include concurrency constraints, channel format support, sample-rate compatibility, or specific flags that are unique to FCP or Motion. That is really good because a buggy or wrong-version MacOS system plugin could destabilize FCP or Compressor. OTOH it's possible auval could pass yet the Flexo AU validation checks could fail. So the above are just attempts to find the problem source, they are not guarantees.