Hey @Torte,
do you have a Premiere or Founder's edition? The buddy passes can only be received in the Stadia App, when you are a founder.
Yeah that's definetely the founder's edition. Did you purchase this via Google?
I think the best option for you would be then to contact Stadia support directly and ask if they are able to send you the Buddy passes directly to the app. Before you contact them, you could also try these steps from the helpcenter to make sure, you have the actual version of the app.
P.S.: Du kannst die Artikel im Hilfe-Center auch auf Deutsch umstellen (ganz unten auf der jeweiligen Seite).