After moving all files and directories from ~boinc to a new partition I had problems getting the boinc-client.service to work on one device. When I ran "systemctl start boinc-client" the process started and a few seconds later I was seeing this:
$ systemctl status boinc-client
[...]
... (code=exited; status=108)

It was possible to start boinc_client as root and then it ran "as usual", although not as a service, so that's not an ideal situation, for after every reboot you have to remember to start it yourself.

In the side panel there was an icon of BOINC together with an icon that I didn't recognize. So I looked in /usr/share/icons/hicolor/48x48/apps/ for a matching icon. And there it was: setroubleshoot_icon.png.

And then it all fell into place, all pieces of the puzzle clicked: the SELinux context was wrong! After setting up a new partition for ~boinc and moving all files and directories to that partition I forgot to restore the SELinux context. So I did
# restorecon ~boinc
# chown -R boinc.boinc ~boinc
# systemctl start boinc-client
and now all jobs under ~boinc are running again as usual.
One of the sources used: https://linux.die.net/man/8/boinc_selinux