Honestly, step back from it all. You've realised you don't need to be on the failure to launch group- great. She's doing okay.
She doesn't want to go to further therapy and enjoys looking for her own solutions. Okay. If further issues develop, then look at them then.
She's enjoying having time alone with you on one night a week- that's lovely, and it sounds like the first time it's happened regularly, so enjoy it.
She's currently cooking for herself, doesn't sound like she's getting into debt, has some savings and is holding down a job.
Where it sounds like she does need you is when the teenage tendancy to over-react kicks in- they all do this, by the way. But she doesn't necessarily need you to babysit her, but instead to tell her to calm down and think about what she wants the outcome to be before she kicks off or does something dramatic.
Thinking back, what might have been a better option than marching down with her to the rent office with the threat of violence? I personally would have told my daughter to stop being silly, as she's not a child or a thug, to go get a cup of tea, and then to call back. Once she's calm, does she need some help getting an email written asking them to check again, can she take a screenshot of her payment going out, take it from there.
When she's threatening to quit her job, again tell her to cool down and think it through. She hates it, she might be better elsewhere, but now she's an adult and needs to think it through first. That means looking for the next job while she's in one, and keeping a bit extra in the bank while she's looking if she can. Your job is to help her see the bigger picture, not to jump to fixing it for her.
It also sounds like she's maybe taken on too much financially with a flat, and needs to think about a house share or similar. I would be selling it as spare money to have fun with , or to book a holiday for later in the year.