I received my letter this past Saturday (2 October), and am now booked in for 19 October!! The letter was dated for 22 September. For those interested in my timeline, I applied on 21 April 2021.
The council said they'd follow up with an email for me to confirm, and they read back the email address the Home Office had given them. I can now see why I never received the confirmation email, and only received the postal notification. The Home Office had the first half of my email address (my name) cut off, and ended it with ".con" instead of ".com."
The end is near! Best of luck to everyone!