Op this sounds really hard and imho you don't need other posters doubting your love for your child. Parents who don't give a shit don't tend to start threads about their dcs.
Only you can judge how serious your dd's mh issues are op, but if she is telling you that she wants to take the pressure off and do a foundation course then personally I would support her in that. The pandemic was awful for lots of teens and young adults and it sounds as though she may be depressed and/or anxious and that needs taking seriously. It is disappointing that the first mh appt is only available in September but good that she has agreed to engage with it.
Obviously, if you think her suicide threats are serious, then you may want to pursue an entirely different course of action, and no one on a sm thread can judge more accurately than you the level of mh intervention she requires, but in your shoes I think I would be encouraging her to go to university, with a lot of support from yourself, mainly bc it sounds as though remaining at home is not doing her much good ATM either. And what do you know about her bf? Is he a good influence or not? If the latter, getting away to uni might be a good idea.
Op you don't need to do anything extreme. Tough love isn't required and nor is pandering to her. You need to step back and support her in her choices and just be there for her (which you are already doing!). It's not easy but concentrate on your relationship. Tell your DD that you love her, even though you are despairing of her in that moment and demonstrate your love for her in small practical ways. Don't listen to her words but try and hear the emotion behind them and respond to that. Instead of engaging in battles, ask her what she needs from you right in that moment.
I totally 'get' that you feel badly about yourself because of all the vindictive things she is saying - I have been there - but please do not take her insults personally. She loves you underneath all the drama but, as you know from your work, she needs to cut herself off from you in order to become an independent individual in her own right. And it can be a painful process but it's a natural one. She's probably terrified underneath the bluster.
Many universities have good mh facilities for students that are more readily accessible then those available at home via a gp for example but at the same time, you will need to offer lots of support, make sure you help her settle in, visit often and take her out for meals, keep in touch and try and make sure she is accessing support.
Don't mention that you are disappointed that she could be doing more academically, even though she is obviously a bright girl. She is seeking to take pressure off herself temporarily and maybe that's not a bad thing? So try and start a new chapter and instead of saying "we will pay for uni but you need to do this, this and this" reframe it as "we are delighted to support your choices , we believe in you, it's over to you now to make the most of it in the way you think best" and make it known that there are limits on your finances.
Watch very carefully what her reaction to this is though, as a lot of defensive bluster and backchat in teens is covering up fear and anxiety and lack of confidence and you may find that behind the rebellion and bravado she needs a lot of support. She obviously needs practical skills too regarding money management, self care, doing her own laundry and cooking so start giving her responsibility for those now.
When one of my teen girls started complaining about meals and being very fussy, (outside of Sunday lunch) I gave her responsibility for shopping, cooking and clearing up for herself and she soon stopped complaining! Backchat like this is often a sign they are ready to step up to more responsibility and if she chooses to eat crap then that's her choice (just leave the odd pasta or fruit salad in the fridge so they don't die of scurvy). Step back and let her take responsibility. After a few months of eating crap she will crave some good nutrition again.
In the meantime, you need to try and step back and support from the sidelines. She does not hate you op, rest assured she loves you, so please don't take her harsh words seriously. At the same time, do not engage in negative conversations. Walk away or walk out of the door if necessary. Make it clear you will engage with her when she is speaking reasonably.
And don't let yourself get so worn down by your concerns for her that you become depressed yourself. I made this mistake and it helps no one! Step back and make sure she sees you fully engaged in your own activities. Take up a hobby or exercise or be out more with the dog! Model reasonable, sensible pleasant interaction. Let her see you negotiate life's difficulties in a rational, sensible way. Be cheerful without being Pollyanna-ish. Let her see you work hard at your job. Let her see you enjoy life! Seek mh support for yourself if you need it. Your DD needs you to be there in the background gunning for her, and she needs you to be strong.
Tough love is not necessary if you step back a bit op because then your dd has to contend with the natural consequences of her choices. Eg, she doesn't have money for driving lessons BC she was sacked from her job. You can sympathise with her and say "oh that's a shame" but beyond that, let her work out the solutions for herself. Don't bail her out.
Good luck op. This period can be so tough but your DD will come through it and out the other side. Keep the lines of communication open but don't allow yourself to be treated like crap either. Try and believe in yourself some more. You are doing the best you can in difficult circumstances. Be strong, and hang in there 
-www.youngminds.org.uk/
-'Untangled' by Lisa Damour
- have a search for the POTs threads on the teenager board on here