I know one of my friend applied 485/765/131 on June 1st (RD) he didn't receive EAD/AP. He seems to be one among the first people who applied AOS. I do not want to disclose any other his details. Point is NSC is lazy not even approved/looked at EAD/AP for the applications received day 1 (June 1st).
Looking at Trackitt.com trackers, it looks like NSC is busy issuing notices for 485 applicants, and not really processing EAD applications that fast. TSC, on the other hand, is slow in sending out notices (currently sending notice for June 26th filers), but is faster EAD processing (first week of June filers are receiving their EAD).
Just a matter of which part of processing does a center think is higher priority. I guess sending out notices does not do anything more than comforting the applicant that their case is in processing. Approving EADs faster can have a life changing impact on a family.