I tested the new VSA 13 with SAML implementation and thought I'd share the process in the form of this little step by step guide.
This guide provides instructions to configure Entra ID SAML integration for SSO access to VBR with version 13
As requirements, you need an Entra ID account with one of the following permissions: "Cloud Application Administrator" or "Global Administrator" for creating a new enterprise application.
You also need a working Veeam version 13 installation.
First, configure the Entra ID application:
Access Entra ID (https://entra.microsoft.com) and navigate to Enterprise apps and create a new application.

Search in the gallery for "Microsoft Entra SAML Toolkit" and select the app

You can specify a name, I choose "Veeam 13 SAML" and then click on create

In the newly created application, navigate to Single sign-on and select SAML.

We now need some information from our VBR.
Open "Users and Roles" settings

Navigate to "Identity Provider" and enable SAML authentication

First, you have to install a certificate, you can either create a new one or select an existing certificate.
I selected an existing certificate.

I did some testings with different certificates but could not see any difference, maybe this is related to "Verification certificate" on Entra.
But for this to get it to work, we can leave this disabled.

Now we do have the certificate selected and can download the metadata to configure the IDP.

Store this xml file somewhere and then upload it to entra id enterprise application.

Leve all settings and just add a "Sign on URL" which is just the FQDN of your VBR. Lets say https://vsa.domain.com

Now we can download the metadata xml from entra id and import it into Veeam.

It should look something like this

Now we need to add the external user to Veeam.


Enter Username or Group name and click OK.
On the login screen on your VBR, you can see a new button "Sign in with SSO"

This will now redirect you to Entra ID login screen. Log in with your user credentials and it will redirect you back to VBR.

If something does not work, here are some troubleshooting steps.
First, Sign-in logs in entra id. You can check if the authentication on Entra ID is successful or not

In Veeam there is this logfile /var/log/VeeamBackup/Svc.Identity.log which can be accessed by enabling ssh to VSA and then reading the file with a command like " tail -f /var/log/VeeamBackup/Svc.Identity.log"
Some thoughts
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In VBR, this is only possible for the web management as well as the fat client (VBR console). The "host management" login is not (yet?) possible to integrate with SAML.
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While testing I found that the error messages in the web gui are not really useful, in the mentioned logfile I found all the relevant information but that is something veeam could improve in a future update