Oh OP, I have a 20 year old with ASD and I don't think you're just her safe place are you? You're her scape goat. It is much easier and safer to just say you've ruined her whole life and made everything impossible for her due to the trauma you've caused than actually face her fears and go out into the big, scary world.
There's no trauma here OP, she's upset that you weren't honest about the assessment, that's fair enough - but it's not trauma. The trauma is facing the real world, facing the possibility of failing, facing the possibility of not being perfect - and that is what scares the hell out of her. Staying home and blaming you for it is what is safe.
She won't speak to her dad because he won't bend over backwards for her, she knows he has boundaries. She doesn't behave like this at baby sitting because she knows it wouldn't be acceptable. But with you it is acceptable, you allow and enable this because you're terrified of the consequences if you don't.
I would try to stop the vague reassurances (or choose to be vague and then explain what you mean by your vagueness so she's prepared for people being vague in the real world). For example 'I'll sort the cake' probably has a very specific meaning in her head that she will think means the same in your head. When it doesn't she gets upset. 'I'll sort the cake and by that I mean I'll either do x with it or do y with it. If you have a preference let me know before dinner.' I'd give her a couple of options with any issue and the time to decide which option she wants to take (time to process sounds like it's probably important to her). There is no choice to just completely opt out and then get upset when you didn't psychically know what she wanted you to do. Remind her calmly and firmly that she had options and a time scale if she gets upset after the event.
You've tried suggesting she does a course with children or with animals but there's no point suggesting things IMO. She won't be interested in doing anything that is not 'the thing' she sees herself doing. You need to find out what that thing is and help her get there. If it's studying finance at Bristol and then you need to work out how she can get there with her. She will need a lot of scaffolding with every step of the way, but if it's what she really wants it will be easier to get her there - if she can get past the terror of not living up to her own very high standards. Break every aspect of moving on down into the smallest, safest feeling steps that you can.
I agree with avoiding punishing her in any way right now. I would also not now start making her do chores for money you've always given her - giving her that for nothing in the first place was a mistake, but she will see it as a punishment if you change the rules on it now. She doesn't need to be paid to help around the house, she's a young adult and should be doing that anyway, tell her you think it's important she starts building her independence and needs to do x or y for herself now. Does she iron her own clothes? That could be a good starting point. Make it things that she will be doing to benefit herself.
Then moving on to what she wants to do with her life. Do you know what she planned to do for uni? Where she wanted to go? Did she want to go to an RG uni? Did she want somewhere more specific that that? What does she need to get there? What access course or foundation course does she need to do? How does she apply? I really think she needs to be saying what she wants to do and she needs you (or someone) to help her get there.
Tell her that it's time now she's a young adult to start thinking about her next steps and you're going to help her all you can. The choices are that she gets a job, looks at college courses she could do or looks at going to university and how to get there - giving her choices will feel like less pressure even if you already know she wants to go to uni. Ask her how long she would like to think about the options and come to a compromise on this. If at the agreed time she is undecided then agree to give her an extension of a week but that after that time if still no decision is made then tell her that her allowance will be being gradually reduced until she makes a decision - because she is a young adult now and adults don't get free money unfortunately or to spend years procrastinating.
If she keeps coming back and back to the trauma and the diagnosis then i would write her a letter clearly apologising for not telling her in advance and explaining (but not excusing!) why you did it. No 'I'm sorry but....'. Be genuinely sorry and then explain why you thought you had to do that and what you hoped would come from it. Then write how wonderful she is and how much you love her. Then move on to how important it is to now start thinking about moving on and her next steps and how much support you are going to give her with moving forward. It may be easier for her to process a written apology and it is something that she can keep going back to.
Good luck OP. Stay calm, be kind, but be firm. I found my autistic teen could be like a toddler in some aspects and sometimes I needed to go back to repeating myself calmly and firmly over and over again like a stuck record until it sunk in.