I work with clever young people typically aged 18 - 25 in an academic environment. We have to provide far more wellbeing support to them than we did 10 years ago. They come a wide variety of schools and universities. My own DD faced difficulties during covid when she experienced bereavement and serious family illnesses within a very short period of time whilst in lockdown.
Several of us have praised the support our YP have received at Oxford. At the open days you will get the chance to speak to current students and the welfare teams at different colleges.
If your DD has no current MH issues, there is no reason why going to Oxford, Bath, Bristol, Warwick, LSE, Hartbury (name any other university) would suddenly result in her developing problems. However, the support system at Oxford experienced by several of us has been extremely positive.
If you Google most top universities you will find reports of misogyny, sexual assault, bullying, racism, classism, plagiarism, AI cheating etc. Sadly, universities reflect society as a whole. If you think about it logically, a story about (say) MH difficulties at Oxbridge provides far better clickbait than a similar story about Newcastle University. Both will equally have students with wellbeing issues.(Not minimising either).