I rarely comment, but I feel so strongly about this! My personal opinion is that yes, you should be paid.
My personal experience has been similar to yours this last year; my partner and I are not married, have two children and I left my job whilst we moved out of London - because of COVID I ended up being a stay at home parent for almost a year. In our case, it made sense for loads of reasons and we agreed for me to have a break from work whilst things settled down.
We are in a pretty unique situation in that when I had my children, I never took maternity leave - my partner took shared parental for 9 months both times. So he knows exactly what it’s like to be sole carer. We have both always said that the one that stays at home has it hardest, so he and I knew what I was signing up for by staying at home.
I told my partner straight away that I would probably be funny about money, I am fiercely independent and it didn’t matter that we have always had shared finances and a joint account with agreed outgoings for children and everything else. I am used to looking after my own money and spending the (little) spare money I had that didn’t get sucked into family life! He was great, told me he wouldn’t question anything, gave money whenever I asked, no questions asked. But he was busy (working two jobs!), I felt like I was bothering him/joint account was empty after I’d done a weeks food shop. I hated it. It really ate away at my self esteem. It didn’t matter how good he was about it, I would have preferred to have agreed a salary to be given on a specific day each month. It would have given me a degree of independence that I sorely missed.
I’m back at work now (thank god!) and got paid last week - it made me feel whole again! Even though I spent part of my salary on things like new school shoes for my daughter (which I could have asked him for, but had been putting off) it felt good to make that choice myself.
Everyone is different, but that was my personal experience. In my case, I wouldn’t be worried about getting married or whatever, because it’s not something I want so it didn’t strike me as useful advice - but I guess it depends on whether you will be staying at home with the children permanently or whether this is fairly temporary.
Anyway, good luck!