There’s no need to stop the VMs if they live in a logical volume and the volume group has free space. You can take an LVM snapshot and use that as the basis for the backup – which you should do anyway, since restic backups are not atomic.
For example, if your servers run a database service and you are backing up the datadir with restic (as opposed to dumping the database using the engine’s dump tool) then you must use LVM snapshots or the datadir will be corrupt.