A discrepancy between the two signals is normal/expected, as audio is a small fraction of the bandwidth to process as compared to video, and the two are taking different 'paths'. If microphone was plugged into camera, then audio & video signal would be processed together and more easily kept in sync.
Typically audio is processed much faster than video, so OBS has ability to delay audio to enable synchronization.
I'm not aware of an automated method to sync these two, so look for methods to figure out the sync delay yourself. You could just play with various amounts of Audio Delay, but I don't recommend that
Personally I used a Ballast Media MP4 sync test video as a test signal/video and found it very easy to use and confirm discrepancy. But I didn't look far/hard for other options, and there are LOTS of tutorials (and other test videos/methods) out there
I personally like the stand-alone video file played on laptop/tablet with camera and mic pointed at it. very flexible, easy to use, no need for Internet connection, etc but your mileage may vary
