Unfortunately I cannot find any information about where the SSL certificate is stored or where I should store my Let's Encrypt certificate. Also in the GUI I can't find a point for this.
Good question. But you can find them in /etc/proxmox-backup as proxy.key and proxy.pem
Have a look at HTTPS Certificate Configuration, restart proxmox-backup.service and/or proxmox-backup-proxy.service when finished and you're set.
You're welcome - and thanks for reporting back.
I've rechecked my own statement from above and I have noticed that a reload of both services is enough. No need to restart them.