After everything else was shown to be working fine (YAY!), Postgres refused to start (don't be thrown by the name - Postgres was packaged as PostgreSQL in praise of Paul Aoki's conversion of the QUEL query language processor to use SQL WAY back in the first packaged release in 1995 - everything but the packaging/branding uses the name Postgres).
This failure to start was not unexpected, though the package COULD have anticipated this for upgrades, since all upgraded installations likely have a need to do this, and run the appropriate upgrade script for us; that script can be run thus:
postgresql-setup --upgrade --upgrade-from postgresql
Unfortunately, it failed.
I followed the trail of error bread-crumbs - a log file in the Postgres user's home directory, pointed to by an intermediate log that's spit out to stdout by said command, pointed to an issue with Postgis, which is used by the installation.
The most pertinent error message said:
ERROR: could not access file "$libdir/postgis-3"
Unfortunately, it didn't say where $libdir is supposed do be, and equally unfortunately, I don't know where it is, either! I haven't yet found any directory containing the name postgis.
I presumed Postgis was not upgraded or perhaps not installed, but that proved incorrect with a simple check of installed packages: It's called postgis-3.2.2-1.fc37.x86_64
As the error message had complained about not finding a part of postgis-3 and yet a postgis version 3 is installed was a surprise to me.
I have no fix yet. Thoughts? This MUST be a common problem for Postgres users who also use Postgis!