Rejections are always hard, even if you know the numbers are stacked against you.
I note the reply th university makes no reference to the students they wrote to with very personal unpleasant (and in fact entirely wrong) negative feedback for this course rejecting them (and that feedback was unsolicited and the first the students heard from Bath) only to be told the next day “oh sorry, we made a mistake and didn’t mean that email for you, and actually you’ve been accepted”.
As a parent I’d say you’ve had a lucky escape from Bath’s messy admin and the personal nasty nature of their first email. Needless to say- whilst Bath had been a first choice it’s definitely our young persons last choice- and with no input from us: she herself says it they can’t get this right, and can be so nasty about it, it doesn’t bode well for the actual degree that she actually has to pay for.