Just adding my experience, I applied for renewal with name change in March. I travel on 11 June. I just received “application being processed” yesterday which I assume from what I read here means it’s going through manual checks.
Every time I call passport office for an update they have no idea and requesting a callback never happens. Apparently I can request a fast track two weeks before travel but based on my current experience I’m not feeling too confident about that one.
Application history
StatusDate
Application being processed 4:47pm on 4 May 2022
Documents received 3:41pm on 4 April 2022
Application received 12:55am on 4 March 2022
Application submitted 12:54am on 4 March 2022