I was just about to call my MP, but thought I'd try the Home Office again. I got someone who was far more knowledgable than the person I spoke to this morning. He explained to me that my application has to be re-escalated as the Home Office hadn't contacted me in the timeframe they promised. He didn't understand why his colleague this morning hadn't done that and apologised that she hadn't. He said he can see on his end that they did email me on Friday, which he said was likely a decision. If they needed something for an escalation they would've called. He apologised to me again that I've had to call again and said I'd have something from the Home Office in the next 24-48 hours.
I mentioned to him what I had been told earlier about not calling my MP and he explained what would happen. Again, this guy was far more knowledgable than his colleague. Basically, because I have made the escalation I'm allowed to speak to the Home Office directly. But, if I get my MP to do it, he said the escalation and my application would transfer to my MP and the communication would need to go through them. Now that I've re-escalated it, if that doesn't happen I'll have my MP take over. If I had known that prior to calling last Friday I would've given this to my MP straight off the bat. I'm not kicking myself for not knowing this, as I feel like I've actually learned a lot about the process and feel I could help others who find themselves in this position by sharing my experience.
Thanks everyone for your support and just being so lovely.
Edited to add that after my MP called, we found out it was an email asking for the death certificate. But, I see the call centre rep's logic.