Am I overthinking this

This recruiter sounds very disorganized. Even if you are the perfect candidate for this position, it seems unlikely the recruiter would be able to successfully bring you along the interview process. I suppose if you have a connection via LI, you could find out more information. I would focus on other opportunities though.
I would give it a rest and keep applying for other jobs. Intentional or not, they don’t seem to be demonstrating interest … also potential jobs mean nothing unless you have a job offer, even when companies say they will hire you, you can only count on a written offer. Your time is better spent applying for other jobs. Right now you can’t keep all your eggs on this one flimsy basket.
I recently had a similar situation with an in-house recruiter. I was so flustered with the disorganization and complete lack of respect for my time (left me hanging for a whole week then scheduled a time last minute when I had another interview booked). In the end, I wrote her back to withdraw my candidacy.