Thanks, Greg. That did indeed fix the problem.
There is something I would add, for the benefit of anyone else who sees the 'Just a Bunch Of Cherries' screen I first posted. If you don't have time to do a new install right away – because maybe you're about to start a gig or session – all is not lost. That 'JBOC' screen means there is a prior instance of the plug-in on another channel. Locate that one and open it, then you'll be able to authorise all instances from there.
Providing you have internet access, it's a good enough workaround until you have time to fix things for real.

Mac Pro 2011, Catalina, 128GB RAM, 2 x 3.46 6-core Intel Xeon, AMD Radeon HD 7950 3GB. Logic Pro 10.6.0.