I was in a similar position albeit for very different reasons.
Scotland here as well. Incase that makes a difference.
Rural community. Due to my job, I found myself when attending routine appointments, feeling extremely vulnerable. I had multiple losses and was consultant led and scanned weekly.
I practice in criminal and family law, with a specific role in safeguarding and representing children in high conflict cases.
Every time I attended the hospital there was a client present, or worse, an opponent.
I spoke to the lead midwife and was allocated a side room on basis of vulnerability. There were two clients in when I had Dd. Many of the staff were also known to me but that was not an issue.
I did have to go to the main ward for a while after theatre and there was an incident with an aggrieved opponent, who was male and the partner of a lady there. He recognised me and called me a stupid bitch, that's fine at work but not when I'm half dressed and bleeding. I was moved immediately and he was removed. I later saw her at court, she was delighted our babies shared a birthday and apologised for her ex behaviour, clearly nothing to do with her but still.
I had second in December, room was allocated without me asking. Marked on notes. This time partners were different due to covid and visiting very much restricted. The staff were acutely aware of the position I was in and absolutely wonderful.
I am probably not explaining this very well but for me, and here, the allocation was based on the exposure and vulnerable side rather than anything else and the staff on the ward were absolutely happy to support that. The partner issue just exasperated things for me as I could glance in a ward and feel safe but then had no control or idea who would appear later.
I suppose the other factor was I was Elcs so in a sense they knew when I was coming and could allocate ahead. Second time I had to wait a few hours for room to be deep cleaned but no visiting was going on and main ward was practically empty.