Hello, I'm also a former Paulina and I did send my daughter there. I think the school has changed a lot in terms of how supportive it is now - my daughter describes it as 'kind' which is a description I don't think many Paulinas from my vintage would recognise much, though in some ways it's the same ethos in the sense that it's a light touch school. Rules are few, the emphasis is on personal responsibility rather than conforming to some outside framework of rules and teachers are prepared to cut students quite a lot of slack on homework and deadlines where they feel it appropriate.
Even though mental health support was pretty much nonexistent when I was there (I don't think that's different for any of the London independent day schools - they were all awful back then) I found it a place where you could argue your corner and be listened to in a way that I think is quite unusual in secondary schools. And I was a dreadfully badly behaved teenager and honestly some of the stuff I got up to would have resulted in expulsion anywhere else I think (I didn't get expelled and went on to a very good university and my teachers were incredibly kind to me even when I wasn't to them). It is MUCH better now, in fact I would say really good.
We are not super-rich and my daughter hasn't suffered from feeling different. The narrative around bursaries is very positive, and aimed at welcoming and celebrating the diversity bursary students bring to the school. There is a huge emphasis on raising bursary funds across the school. DD has plenty of friends who are just ordinary kids with normal parents. We have found very few of the super-rich among our friends and acquaintances at school. I do hear stuff about other girls on occasion, but I don't think it was hugely different when I was there. I don't think I personally noticed the disparity in wealth until some time after I joined, tbh. I was just an ordinary middle class child, because as @Pleasegrowmore says in those days normal people could afford the fees.
I would heartily recommend anyone thinking of whether they would be eligible for a bursary to just ask in advance of applying. The school has bursary funds to spare - not enough people are applying for bursaries and they want more!
I know there is another former Paulina who has also sent her daughter there on MN, and I have had some interesting conversations with her on the subject of how it has changed and how it hasn't changed.
So there you go, not all former Paulinas want to avoid St Paul's at all costs.
Re 'why would you even apply when you can go elsewhere and get the same results', I didn't send my daughter there for the results as I'm quite sure she would have done really well at the local (pretty decent) comprehensive. And she also got into Tiffin which is obviously free. I sent her to SPGS because I liked the culture and the curriculum and because having experienced SATs I did not want her to spend her school days as a data point. There was other stuff too (specific to her) which made me think she would like it better there than anywhere else. And she loves it.