Found a solution! All you have to do is to make a security policy that disables showing the last signed-in user. This defaults the sign-in screen to "Other user" and allows Veyon to correctly enter the login details. This is also better for privacy because you don't see the info of the last person that used the PC (Admins can still see in azure or some other admin panel, it just makes a visual change to the login screen.)
In the Master settings (in Veyon Configurator) you can configure the "Feature on double click" (https://docs.veyon.io/en/latest/admin/reference.html#behaviour) to be "Remote view" or "Remote control".
We see the exact same behavior. Win11 25H2, wired network, no firewall between master and client. Veyon-Version 4.9.8. The image on the master-pc freezes, not on the client-side (the headline is misleading).