My VAWA was approved more than 1 month ago, USCIS sent only C-31 EAD without approval notice. After 4 weeks waiting, I reached out to my senator to help request my approval notice from USCIS. USCIS responded in a week saying that they have issued my approval notice — that was when my case status online finally changed to “Case Was Approved.” They also said they sent my 485 to NBC within 1 month of VAWA approval — I haven’t seen any activity on my 485 yet, still waiting!
You need your VAWA approval notice in hand. I would advise you reach out to your congressman to help request your approval notice. If the current status update on your approved VAWA means anything (which I don’t think, probably a glitch or someone touched your file), they will tell your congressman in their response. The update on your 360 may also be as a result of the recent 485 inquiry you made with USCIS rep.