You all need a reset but how to achieve that?
I must say I can understand that your dd is angry about being hoodwinked into a diagnosis, especially if her mother (parents?) have a tendency of being avoidant.
This may sound a little harsher than the other posts but perhaps it might help see things in a different perspective.
Your DD has extreme black and white thinking and an enormous desire / need to feel in control. She trusted you when she went for that assessment and came out of it having been diagnosed with ASD when she felt she had no control over the process experience or outcome whatsoever. Essentially this was 'done to her' and changed her life. It undermined her autonomy and feeling of being in control which I believe can be particularly import for autistic girls. If she has problems with identifying her feelings then the enormity of the diagnosis would have been impossible to process.
I am guessing that the reason you didn't tell her at the time was due to being avoidant. You didn't want to deal with her reaction or refusal and tricked her (not judging you just observing). The cake saga also has avoidant personality written all over it. Letting her call her sister 'it' is so very unacceptable and how the family are dealing with this also seems avoidant.
The problem with this is that you have accommodated her wild expectations (various cakes in certain sequence) when what she needed were firm boundaries as well as genuine empathy and helping her understand her own though processes.
If she has OCD this may need to be medicated but if it's not at that level, you could have tried saying that you understand she want the cakes in a certain order and why she might find that idea comforting or appealing but that in the reality of family life during COL buying several cakes is not achievable and is actually a 'bad' / negative thing even if it seems appealing. It was avoidant of you to promise a second cake rather than dealing with her stubbornness and outbursts.
I am also surprised she has uncensored access to the internet. She is an adult sure but I'd limit access to WIFI and internet to a couple of hours a day. If she can entertain herself in her room she will feel no need to tackle the world and her life as it's all safe and comfy and she can control her family at the click of her finger.
So my suggestion is stop being avoidant as avoidant parenting will make your dd feel unsafe and undermine her need for honesty and transparency.
Being avoidant is in essence quite manipulative and controlling just in a different way. Not the typical authoritarian control where the you would dictate every choice but controlling in a passive, indirect way. It leaves your child feeling like they can’t fully trust their environment and like their own emotional needs are secondary to the parent’s need for peace or avoidance of discomfort.