I can’t really answer your question but I did the same for my son (the guidance is rubbish and I was in auto pilot). I called the passport office number, they just advised me to send an accompanying letter explaining why signed by my son. I haven’t heard anything back. The application was sent on the 12th May and the letter was acknowledged on the 1st of June (arrived the 20th of May).
It’s all super inconsistent and the lack of any advice on what’s going on is so frustrating.