I've got the same issue. And also contacted Apple. And as always they responded with some dummy helpless message.
However, I was able to solve it myself.
After my app got approved for internal testing (after two days), I've created a group for internal testers and added myself there as well (add new user). That user also had "No builds available" status.
However, in the Internal Testing group I've created a Public link and clicked "Send invitation to all testers" link there.
After that (magically) all and not only the testers from the internal group, but also App Store Connect Users became having "Invite (Resend Invite)" statuses.
So... hello Apple! (Still waiting for "solving" the issue from them...) )