Ah, well, that broke things.
I did:
yum upgrade mysql --enablerepo=centosplus
It did upgrade MySQL, and I can log in to MySQL and it seems to run fine. However, the server-manager/ URL is broken. Apache reports a 500 error. Looking in /var/log/httpd/admin_access_log I see errors that look like:
Premature end of script headers (index.cgi)
Can’t do setuid (cannot exec sperl)
I'm looking into it to see if I can find out what's going on...