10.4.6 is before the Metal optimization work that began in later versions. 10.4.10 will be significantly faster on certain tasks, especially encoding and effects. Before upgrading, ideally make sure all libraries are backed up, and in Finder make a duplicate copy of the Final Cut Pro.app file in /Applications. That will allow easy rollback to the prior version if you encounter problems. Make sure all plugins (esp. CoreMelt) are upgraded beforehand. You can stay on Mojave if you want.
Make sure Chrome is not only closed but totally not running — not in memory at all. Verify with Activity Monitor. It is safer to just not run it, since it mis-uses the MacOS VideoToolBox framework and can unpredictably cause slowdowns, hangs and crashes.
A 30-second beach ball or spinning wait disc isn’t like a slow progress bar. Rather it indicates the main application thread is stuck in a code path and has stopped responding to events. It implies something is wrong such as a system-layer issue or a buggy plugin which deranges the FCPX process.
Make sure you have plenty of disk space, and try disabling background rendering, then delete all current render files via File>Delete Generated Library Files>Delete Render Files>All. Thereafter render the timeline manually as needed by doing CMD+A to select all clips and CTRL+R to render.