They really do not share any updates, so there is nothing to anticipate/ worry about.
You can expect the passports to reach you in about a month from when it reached them. Expect to see updates to the shipment tracking status around June 9th.
Received my passport and PCC today (5/30), the application had reached the SFO consulate on 4/27.
Being more precise, the application was through mail and my passport was issued in SFO within the last 5 years.