I tried to signup at gitlab.com, but entered a faulty email address.
Apparently email addresses without a top level domain (dot sth.) are accepted.
Now the signup process is in limbo, and consequently the proclaimed user name is marked as taken.
My question is: What happens next? Is the user name going to be released at all, if so when?
This is a community forum, so nobody here can help you with account issues. You’ll need to open a support ticket directly with Gitlab so that their support team can resolve it: https://support.gitlab.com/hc/en-us/requests/new?ticket_form_id=360000803379
The username is taken because it was registered, irrespective of the wrong email address being supplied. They are not released, ever. When you open the support ticket you may be lucky in that they will release it for you, or at least allow you to provide the correct email address - assuming you can provide the incorrect email address that you gave during registration to verify/prove at least that you tried to register that username.
Failing that, you’ll just have to create a new account with a different username, and ensure that you complete the email address details correctly before submitting the registration.