FWIW:
I think they have been advising overseas applications would take 13 weeks.
My fiancée made an overseas application for her first British Adult Passport (citizen from birth but living abroad). Exactly 13 weeks to the day since “Documents Received” (“Application Processing” no longer showed as is the case for many others) she got an email asking if she was in England or abroad. Confirmed abroad, and then they said they’d continue to complete the application. Today they asked for a photo of an ID card which was provided. The passport has been marked as going to print today also.