is your home folder actually under /var/home/… not under /home/… ?
Yep, it’s how Silverblue is set up
$ ls -l /home
lrwxrwxrwx. 4 root root 8 28 janv. 13:51 /home -> var/home/
does the scripr run correctly when you paste the full path in the comandline?
Yes
From what I gathered from the comments, system services cannot access the home directory by design: user services should be used instead.
But since it is nearly impossible de execute a user service on shutdown, I changed my approach and went for a user service and a timer that initiates a backup every 15 minutes. Since the backups are incremental, it shouldn’t take too much time nor space.