Perhaps my installation has quirks that either cause this problem or contribute to it.
What happened previously from time to time was that the file /etc/resolv.conf would be deleted somehow, breaking name resolution. I keep a backup copy of that file and restoring it is easy.
When I updated to openmediavault 5.1.3-1 this morning, resolution broke again so I tried to restore the /etc/resolv.conf file. However, this did not work because /etc/resolv.conf does exist but not as a file. It's now symbolic link to /run/systemd/resolve/resolv.conf. I believe this linking is more in line with how Debian does name resolution on Buster. The problem is that the directory /run/systemd/resolve does not exist. I created it and placed a copy of the file resolv.conf in it and resolution now works.