I have a similar issue. Applied for a first UK passport for myself and my daughter on 26/4. Sent both sets of documents in the same envelope to Corby (with both reference numbers displayed on the envelope). My documents have been “received” on the 2nd of May, but there is nothing showing for my daughter. This makes very little sense, as you’d think that the documents sent together would be entered in the database at the same time.
Please let me know how you get on. My daughter needs her new passport for a school trip in early June and I’m really worried.