Recently things have changed a bit additionally, since we are backing Postgres up directly on a Synology NAS onto that NAS now. So there's no additional fully blown Linux/Windows host copying things to some share or stuff, but instead the NAS itself executes scripts taking care of pg_start_backup, copying things around etc. simply using SSH.
What is PostgreSQL disk topology -- file system, local storage or using the NAS? Have you looked into snapshots?
I already read that the exclusive backups we take now are deprecated anyway[1] and that shared backups need an open session during the time of the backup, which makes custom scripts additionally difficult.
Here’s an example of a bash script using a pipe to issue the non exclusive start/stop backup command: