and say bounce the database server and install the binaries. What I have never considered before, and I should have, is the complexity of doing this for many remote servers. Can we improve our guidance for these cases?
What guidance is needed? Even for us, where firewalls block our servers from https://download.postgresql.org, it's as simple as downloading the relevant RPM files once (and that done with a PowerShell script), then patching thusly:
WinScp PG16.4_RHEL8 dir to each server, and on each server