How long after you’ve passed the NCLEX, is your license number posted to the state board of nursing website? I’ve started applying to nursing positions, but not sure if I should stop and wait until I receive my license number.

It depends. I had to wait about a week for my license number to be posted. I was told it could take up to 30 days till I found out if I passed. Keep on job hunting. If you got a job before your license number is posted, they will hold the job for you.

in 24 hours the RN-LPN licenses are ready to verify

Definitely apply. Interm Permit given to those whose status is pending.
(I would think in one week and you should know if you passed

In the state of NY in 2014, it took several days for my license to appear on the Office of the Professions site.

Just check it on nursys.com