The school has shrunk a bit since my year 4 started in 2021 but I would say I knew parents from each family across all three of my children's classes well enough that I could tell you their job or if they were a stay at home parent.
It's a small village school (one form entry, classes no longer full, although over subscribed when my older two were there) with not the best wrap around, although it does have it.
Mostly parents work but work around pick ups and drop off and it's typically parents who are doing those school runs. Sometimes grandparents. There is the occasional nanny at the gates (I can think of one family in the school currently using one), previously there have been two others. Most work. It wasn't uncommon to see people trying to keep themselves online on Teams in the end of term church services! Some parents split pick ups (parent one drops, parent two picks up), some use wrap around but it only goes until 5. I know of several who nip out to get the kids and dash back to log on. Several work for family businesses which offers flexibility.
I have one child left at the infant school and in that class there is an older parent (mid 50s) who does not work and one other who doesn't work but has a preschooler and is considering what to do come September. There's two on maternity leave (one will 100% return to work, the other I'm not so sure). Everyone else works. Most parents in the class are actually older. There's one who is early to mid 30s. The rest are all late 30s upwards.
Edited to add: Most people drive to this village school as it wouldn't survive on just the young families in the village. For a 3 bed house you are looking at probably about £420,000 in the cheapest near by town. In the village itself you are looking at about £700,000 and in other surrounding villages about £550,000! That probably explains why so many work!