The current pre-release of the client ("pioneer" in the version) is only compatible to itself. So you can only play with other testers. Please be aware!
It seems like that was the issue, though I don't know why.
I fixed it by going into FAF settings and ticking Vault Fallback Location.
Rebooting my PC, updating FAF to latest, updating graphics drivers, updating Java and reinstalling FAF (though not redownloading everything) - none of this worked.