There is a lot to unpick here. I really empathise with and understand how overwhelming it can feel.
A key starting point is to help the school to understand that they have inadvertently conflated two things: autism and gender identity. Perhaps there is a way to bring them on side to your watchful waiting way of thinking by helping them to see the significance of the new ASD diagnosis. At the moment they seem to think that they know best but they have a huge blindspot here. Have you seen the Transgender Trend information on autism and gender identity? It's got lots of useful information that unpicks the conflation, plus some useful links to research papers at the end.
https://www.transgendertrend.com/autism-gender-identity-introduction/
In addition to the Interim Report from the Cass Review, I used the Tavistock research paper that showed that 48% of referrals are autistic when I spoke to my daughter's school about safeguarding. That is far too high to be an acceptable coincidence. This paper is referenced in the introduction on the link above.
Depending on your child's needs, they might benefit from an EHCP. At the very least, it sounds like they would benefit from safeguarding around gender identity. Prior to getting it in to my daughter's EHCP, I wrote a safeguarding statement that I asked the school to follow so that she didn't get pulled towards the idea that she was trapped in the wrong body. Perhaps this is something that would work for you too?
You mentioned in your post that the school is now using new pronouns as well as a new (nick)name.
Will you be asking the school to revert back to your child's sexed pronouns? Have you felt able to speak to your child about why it's important not to make any changes from sex based pronouns while they understand themselves better? Whenever anyone asks my daughter what her pronouns are (I really wish they wouldn't... asking the question is effectively asking "I can see you're a girl but are you happy being one?". Sadly it happens a lot when they see her short hair and "boys' clothes") she either says "I don't know" or "I don't mind". Depending on the person, they either move on or, and I've had to intervene directly on this in the past, they say that they'll use they/them for her. I am mindful that I don't want to push my daughter away from trusting and confiding in me, but I am making it as clear as I can to her that while she's understanding what gender identity means to her, it is important that nothing changes. She uses a neutral sounding nickname but that's very different from changing her pronouns. The Cass Review, mentioned above as well by a PP, makes it very clear that social transition is not a neutral act and that autistic people are particularly vulnerable to locking in on an identity as an answer to any distress that they might be feeling about their body or who they really are as a person.
I'm not pushing my own views about gender identity belief on to my child but I'm safeguarding her as best as I can from being pulled towards the bias that could lead her on to an affirmation pathway. It's a very difficult line to tread, making sure that I remain neutral so that I don't get cast aside as a "bigot", and having the school on side is an important part of it all.
If the school won't accept that this is a safeguarding issue and that they need to unpick autism from gender identity, I would personally move my child elsewhere. Otherwise, everything that they do will continue to be from a affirmation perspective and will inherently bring in the bias that your child does have a gender identity (representing belief as fact) and that this needs to be affirmed before anything else is put in place. This is not a safeguarding approach.
From my own experience, I would caution against autism parenting support groups as there seems to be a general acceptance amongst them that having autism and being trans identified doesn't raise any alarms.
Is your child male or female? The conflation of autism and gender identity seems to follow general patterns in line with sex. This is also something that may be helpful to point out to the school.