Equity does not allow videos to be used to take notes on a performance. It's only been recently that stage management has been allowed to have the archival videos on hand for understudy and put-in rehearsals, and even then that's not something that's been allowed in every contract yet.
As far as resident vs associate, my experience has been that they are merely contractual terms. There are not really set standards for their duties, so it will vary from production to production.
Call_me_jorge, those videos you linked demonstrate what we've been saying. The original teams may still check in on the shows from time to time and then give their notes to the appropriate person to disseminate to the cast. In the Matilda video you see that it is the dance captain who is running that note session.
In the Wicked video, the Joe that Marybeth (the PSM that video has been following) mentions is not Joe Mantello, but the carpenter who made whatever adjustment was needed to the bed. And earlier in the video you hear Rondi Reed and P.J. Benjamin talking about her giving them notes.