Mh that sound's weird @Bork.
I would recommend to try these steps to try to fix the Stadia App. Check after each step if the second buddy pass is shown.
If this doesn't help, try to contact Stadia support to receive help in this case. Maybe they can provide you more steps or maybe an alternate code or something. It might also be, that the first Buddy has to accept the invitation or use the code, before you can prepare a second one, but that's just a personal thought.