Hi again,
following the advice Update failed (postgresql) - #8 by noezDE by @noezDE (thanks a stack!), we have been able to recover from this situation.
Now, the site is running again and we will look into upgrading once again.
With kind regards,
Andreas.
Recovery procedure
At first, progress was made by invoking
chown -R postgres /shared/postgres_data
sv restart postgres
After that, the logs said
2021-10-13 18:52:12.437 UTC [3357] FATAL: could not create lock file "/var/run/postgresql/.s.PGSQL.5432.lock": Permission denied
So, we went full-on and invoked
chown -R postgres:postgres /shared/postgres_*
sv restart postgres
Voilà.