Security Update 2020-001 (Catalina) and 2020-007 (Mojave)

Might be reindexing Spotlight? In which case it will self-resolve.
I haven’t noticed any major slow-down with my Retina Macbook or iMac.

Well, I wouldn’t think so, since it had been a week since I had installed the update. But maybe Spotlight felt like the time was ripe. Certainly it seemed to self-resolve.

Just to be clear, the slowdown was only on shutdown and startup, not during normal use.