"Nobody has ever asked me whether I work or am I planning to return to work or anything like that"
That's really, really unusual OP. Whereabouts do you live? I assume your kids are teens: is it still the norm young mothers don't work in your area?
I have a 3 year old and am pregnant with no 2, and my social group is the exact opposite. Of the women I met on maternity leave I'd say I'm in about 3 WhatsApp groups comprising a breastfeeding support group, people who met at baby class, people who live near me totalling about 50 women who I'd 'know' at a v surface level, and would have made lots of small talk with. I honestly only know one mother out of those 50 who didn't return to work after mat leave on her first, though some did go back part time. I'll be curious if that number increases now they're all working on number two, though so far it hasn't. In my wider circle of family I know a few stay at home mothers but tbh they're still massively in the minority.
In conversation, if it came up, I'd probably say something like 'there are really few stay at home mothers near me, though a lot of parents seem to work from home'. I think I would say something like 'oh Sarah is a stay at home mum' if it was relevant.
I've definitely referred to stay at home dads, and stay at home mums, when referring to real people. I'd also never 'say' an acronym, like 'WFH' - I'd always say working from home, and that's what I say in my head when I'm reading things out. Similar with stay at home mums and stay at home dads. Its just typing shorthand. But the terminology is real, and yes people use it in real life.