The file (socket) for supervisord is, as expected, in /var/run/supervisor.. the pidfile is in /tmp

Leaving files in /tmp relating to a build is also not great.

If it were in the standard location, which is still configured in /etc/supervisord.conf, there would be no confusion and less to change when fixing the container so that it does not run processes as root

Sorry, but I still don't understand you. File permissions is a separate issue. This ticket is about the usage of /tmp instead of /run. Is there anything that prevents you from changing permissions on /tmp/supervisord.pid that would work on /run/supervisord.pid?

PID file location was changed by : https://github.com/percona/pmm-server/pull/92/files#diff-1c132cd2582dfc6eee14e5064b7fbd4fR10 Probably he can explain why he made this change.
We still use the same path in 2.x: https://github.com/percona/pmm-server/blob/d35b429475ec8d9d0799c5b6ca28134b171e2252/supervisord.conf#L8

We support the rootless container in MS and were forced to manage permissions on /tmp/supervisord.pid because it is present and owned by root in the container:

Mounted PMMv1 container

It appears that you have stopped this happening in 2.x:

Mounted PMMv2 container

Please explain why the default path was changed in the first place.

I read it before commenting. I still do not understand why the usage of /tmp instead of /run is a problem.

please read the ticket that this triggers