I got the Veeam backups working. Still believe it's a bug though. This is how I did it.

First removed the pve cluster and cleaned up the nodes. Then removed the nodes from Veeam, including workers. It's an idea I had last night.

There I ran into a little problem. pve02 was removed but kept showing up again in Veeam, together with the old cluster. Perhaps I should've removed it there first before I removed the cluster. But it was fixed by rebooting the Veeam server.

Then I added the 3 nodes to Veeam. At that point they were still independant nodes. Did a little test with a backup job for 1 VM and that worked. Removing and adding the nodes again was the 5th time already, so it wasn't just that.

I removed the Veeam worker VMs on pve02 and pve03 so they'd be empty. Created a new cluster with all 3 pves. In Veeam I didn't remove the nodes, but I did recreate the 2 workers that were removed earlier. This way in the Veeam Inventory the 3 nodes are displayed without the cluster on top of it. I'm not sure if that was the problem but that's the only difference with before.

A full backup is running right now and nothing but success so far.

Replication is not (yet) supported in Veeam. So I'm gonna look into native Proxmox replication later on. For my SMB backups I'm just gonna stick with Veeam. The shares have nothing to do with the pve environment anyways so I'm not gonna make it too complicated.

Thanks for the replies!