Mate Desktop in an Apptainer container?

Off the top, I’d suggest adding /run into the container. Maybe /var as well.

Seems like you can’t communicate with dbus correctly and I know those are important directories.

A google search of the error seems to indicate there’s a library issue. You’re using centos 7.9 container, what’s the host OS? Maybe there’s some mismatch or some missing package. That file seems to come from dconf itself so I wonder if it was missed somehow?