The following xmllint XPath query will pull out the name of the backing file for a VM named fedora-server-36 and an external snapshot named fedora-36-post-install,

virsh snapshot-dumpxml fedora-server-36 fedora-server-36-post-install | xmllint --xpath "string(//domainsnapshot/disks/disk[@snapshot='external']/source/@file)" -

The string function extracts the attribute value.

This value can be used in the process of using or deleting the snapshot.