Issue with WD My Passport, Mac not enabling mount of a previously perfectly working external hard drive configured for Mac.

Was Final Cut Pro accessing the disk when it was sluggish?

Sluggish disk access is one possible symptom of a failing hard drive. If it can't write, it will try over and over which appears as sluggish access to the drive.

All the other symptoms tend to point to a failing drive, too. It is quite possible it is something else, but I don't know what.

I would agree is sounds like a failing drive. BUT ... I would let First Aid run overnight, as you are using a few TB and First Aid might take a long time if the file structure is complex or there are many small files.

You could also invest in a different disk tool, such as TechTool Pro, but that will cost a good fraction of a new drive. However some disk tools can fix things others cannot. If the drive is HFS+, DiskWarrior can also try to repair it. Such "repairs" are file system or file catalog repairs; if the drive is experiencing a hardware failure, it is gone.

If this is a backup drive for Final Cut Pro, I would personally replace it. A backup drive has to be bulletproof reliable. This one is one I would have doubts about.