When you change the certificate of the Proxmox Backup Server all the nodes will suddenly stop making backups without warning. If you click on the storage for the backup server you will see an error that says the fingerprint has changed.
For an internal LAN you probably don't need to worry about the fingerprint changing. If you do, you will have to modify the value each time you update your Let's Encrypt certfiicate (i.e., every two months).
To ignore the fingerprint open /etc/pve/storage.cfg and look the section with your backup server definition. It will look something like this:
pbs: proxmox-backup
datastore backraid
server pbs.mydomain.ca
content backup
fingerprint f4:b3:c2:64:87:82:7d:a5:be:54:e2:a4:8a:1c:a7:23:aa:36:0b:a8:2a:a6:55:d9:18:de:55:6d:73:20:5a:9d
prune-backups keep-all=1
username admin@pbs
Remove the fingerprint line and you will no longer have to worry about updating it every time the certificate is updated.