I feel for you OP as I always felt the same as you. I worked full time, so rarely could do school pick ups. When I did, the other mums were polite and acted friendly, but none would include me in their group conversations etc. I’d be stood on my own nearby, having smiled/waved/said hi (to which they’d all respond but then would keep their backs turned to me slightly, wouldn’t say anything further to include me, etc). I always felt like my kids weren’t invited to parties etc because they didn’t like me. I’d invite their kids for play dates, they’d very occasionally happen but most of the time there would be excuses made.
I wasn’t aware of any class WhatsApp groups - but then during Covid, I was added to a WhatsApp group with the other mums from my youngest son’s primary class. Great I thought. Except then the person posted to say basically sorry for setting up the second group, but not everyone was in the original group… then went on to ask us all to make a donation towards buying some hampers for the teachers. So I was good enough to be asked for money (and they had my number) but they’d never wanted to invite me to join the class WhatsApp. Had I been aware of it, I could have asked to join - but I didn’t know it existed! I was really hurt.
I don’t have any words of wisdom as it still hurts to think back to it now. I am currently on a waiting list for ADHD assessment, and I suspect that maybe if I find I am, it would explain why I struggle to fit in. I’ve always thought of myself as kind and a people pleaser - I’d always do whatever I can to help someone or be there if needed, that kind of thing. I don’t go around badmouthing people, I don’t gossip, my eldest and youngest were exceptionally well behaved (middle son as always a nightmare, but that was more that he was a handful as suspected ADHD & ASD - he wasn’t a horror, just hard work)…. I always looked much younger than my age, and although I was 25 when I had my first, I looked significantly younger than all of the other mums, so I wonder if that was anything to do with it.
I think the only thing you can do is keep inviting your daughter’s friends for play dates. It sucks to always be the one to make the effort, but it might be the only way you can do it. Look at clubs, see if there are any she might be interested in joining. She might make friends there that aren’t from her school.