I doubt that Synchronize Folders will do what you want, it will also remove from your Lightroom Catalog any photos that are not in the folder Lightroom Classic thinks it is in; and this is NOT what you want.
FWIW I do exactly this as part of my backup routine regularly (and also to let me work on two machines), but on Windows. It has been very reliable and I never had any problems.
I use special file synchronisation software to streamline the process, which means the "transport" drive does not need to have the same name (or drive letter, this being Windows). This added flexibility should be well worth the small cost.
As long as the source and final destination drives are identical, the catalog correctly picks up the files from the destination drive.
Precautions: I run the process in one direction only, never in reverse, to avoid any corruption spreading (there hasn't been any). I also back up the catalog separately using the built-in routine, since the synchronisation treats the catalog as a single file, completely overwritten every time.