macOS Sonoma caused Final Cut Pro 10.7.1 to struggle with 4K playback?

Try creating a new admin user. Disconnect all the external drives and assorted hubs. Import media into a new library in the new user working only on the system drive. See how the application performs.

After trying what Tom suggested, if the beachball hang still happens, while it is hung, do these commands. It doesn't have to be the same hang event, but make sure FCP is hung in the beachball state while each of these run, which takes about 3 sec each.

These are built-in MacOS commands to sample data from the hung app and produce TXT files you can submit or post somewhere we can get them.

The first command (spindump) samples the hung process every 10 milliseconds for three seconds, creating a list of each thread's call stack, ordered by the number of times the function appears over the sample period.

The second command (sample) also samples the hung process every 10 milliseconds for three seconds, but it writes each sample to the output file. This enables post-processing of that file to examine the execution frequency of each function in each thread's call stack over the sample period.

The spindump file will be about 10MB and the sample file about 2MB. They are TXT format, but too large to post.

I can analyze these and hopefully get an idea of what FCP is doing during the beachball interval. You will need to upload them somewhere we can get to them.

sudo sample 'Final Cut' 3 -file ~/Documents/FCPSample3s.txt

sudo spindump 'Final Cut' 3 -file ~/Documents/FCPSpinDump3s.txt

It helps isolate the problem if you duplicate your timeline, open that duplicate, select all clips with CMD+A, and then do Edit>Remove Effects. Then, see if it's still slow. If it's fast and smooth, that points to an effects issue.

If it suddenly becomes fast, do CMD+Z to under the Remove Effects, then select 1/2 of the timeline and do Edit>Remove Effects and try that. Repeat that process using 1/4 then 1/8 of the timeline until you narrow down the clips and effects causing the problem.

Some effects, such as Neat Video, are simply compute-intensive and will be slow unless the timeline is rendered to cache. Some combinations of optical flow retiming and stabilization can be slow. The object tracking feature in some cases can be very slow.

It's probably better you do the above tests and report the results before gathering that data using the scripts I listed above. (Never mind, I got the files you uploaded).

There are a lot of calls to the MacOS Espresso AI framework. Are you using voice isolation or the object tracking feature? If you are and you know what clips those are on, can you disable those clips and try that.

There are also lots of AU (Audio Unit) related calls in the hung thread. Are you using any 3rd-party audio plugins? If so, as a test can you try disabling those clips?

This is just an early observation, still looking...

Try running the Terminal scripts joema shared and post the results.