It's definitely not the easiest to sort out when it comes to HMRC. My P85 has been received but when looking at their response times they said it could be the 17th January 2025 at the latest that I get a response regarding it.
I do have another issue with HMRC though where one of my previous employers has duplicated my salary and tax paid resulting in them thinking I haven't paid enough tax (about £1k) for the tax year 2022-2023 so after having speaking to them, I have contacted my employer at the time and asked them to amend their RTI submission. They haven't replied to me yet after 3 working days but my manager from my time working there has said she is willing to help get this sorted out for me which is good. HMRC have put the case into query for 6 months while this gets sorted out as well.
I'm glad you have managed to get some things sorted out now as well. I have been added to my fiancees Gas+Electric bill, Water bill, Credit Card and Costco Account (not that this one is too relevant). Got my SSN appointment next Monday and then once I have received that I will look to get a bank account. Also in the process of scheduling our wedding ceremony.