The login queue not moving is an issue that has popped up throughout all of Final Fantasy XIV’s most populated times, but it does not mean the queue is broken nor does it mean you’re stuck there.
It appears that the login queue not moving is simply a client-side bug, or perhaps there really are that many people not logging out. The former seems more likely: once your queue position starts to tick down on your client after sitting at the same number for a long while, it does so quickly to tick you down to the place you are actually sitting at in queue.
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Don’t get impatient and leave the queue while the login queue is not moving. It is not stuck! Just be patient, and you’ll see it start to tick down in time. Final Fantasy XIV reached its peak player numbers this past summer and Endwalker is its biggest expansion launch yet. Queue times are guaranteed to be long, at least for the first week or two.