I advanced to the reference-checking point after a job interview. How long should I wait before reaching out?

I got interviewed Tuesday morning and was told that if I were to move on to the next step, it would then be time for reference checking. 4 hours after the interview, I received an email telling me it was time to provide references on a system called skillsurvey. My 6 references responded within 24 hours. Where do I go from here? How close are you to getting hired once references are getting checked after the interview and when, if at all, should I reach out?

Side note- the interviewer also brought up another position and asked if I would be interested and I said I would also be interested in that position (just to be more flexible).

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