I suspect whether you have the option of single sex state education will depend on where in the country you are and the policy for that area.
I went to single sex for secondary. It was a smallish town with a rural catchment, and there was no choice unless you went private.
We knew lots of boys because we'd been at school with them since primary. We saw boys on the school bus, at swimming club and other activities. We shared with the boys school for some things like drama productions and language exchanges. Half my 6th form lessons were st the boys school, because the only way they could run some A-levels was to share numbers.
Academically, I didn't hear stereotypes like "girls can't do maths," and the stats on girls doing more STEM subjects in single sex schools- we fitted in to that.
Yes, there was some bitchiness and there were different groups, but teenagers. You get bitchiness in mixed schools, too (and boys schools, they just don't call it bitchiness.) I wasn't really aware of bullying - that happened more in lower schools/school bus, IME.
I'm still friends with people from school, 36 years since we left. Had I had daughters, I'd have preferred single sex secondary for them. I now work in IT in a very male-dominated sector - I am literally the only woman in the room. I can communicate with them with few problems (certainly better than some men around here.)
But school choices still depend on the child and the school - what works well for one child won't work as well for another, even in the best schools. Outside of school - you might choose Guides, or you might choose something more mixed to counter the lack of boys at school. It's not just school where you meet people.