OP, I think your worry is understandable but you need to do your best to dial it back a bit as she is probably picking it up.
She sounds like she's not very resilient. which, if she was previously bullied, is easy to understand. Also, remember that a lot of children who were starting school at the time of Covid are widely acknowledged to have missed out on some really important social skills and social development.
DD is also not as resilient as I would like and we've had to work quite hard to get her to be able to understand and be less black and white in her thinking. eg, if she says that person X said YY and that means she thinks that's it for their friendship, we'll talk about why that person may have saidi that, what might be going on in their lives, and whether this one thing makess all the other good things about them less important.
DD loves dance so she attends a lovely dance school. She hasn't made very close friends as, by pure bad luck, she's pretty much the only child in her year group in the school! But she has made friends and being there makes her feel good, gives her a sense of purpose and community, and that helps her with her confidence elsewhere. If you can find something similar, that is helpful. Also things she can be passionate about will help her make friends, especially as she goes into high school, as she meets other people with similar passions.
If she won't see a counsellor, can you discuss it with the school - many schools have informal counselling or guidance programs or can even do things like encourage certain friendships etc. Does she have a teacher she particularly connects to? That can be very powerful too if you have a word with that teacher.
Finally, it is interesting thatyou sensed smoething and went with an ASD assessment. is she also being assessed for other ND such as ADHD, SPD etc? Any and all of these can impact how a child interacts with the world.