potential downsides, including stigma and how labels can shape how a child is treated
If your daughter is not autistic, the assessment will find so.
If she is autistic and assessed, she gets a diagnostic label of "autism" that explains to her and everyone she chooses to disclose to that she's neurologically different and what can be done to make her life and the lives of those around her easier.
If she is autistic and not assessed, the labels she gets are "thorny", "rude", "bad-tempered", "flakey", "weird", "unreliable", "over-sensitive", both of "too quiet" and "talks too much" because she doesn't know when to speak, "manipulative", "arrogant", "naive", "needs to toughen up", "needs to become more streetwise", and "brings trouble on herself". She spends her life failing to understand why she doesn't understand other people, trying desperately to be liked and pushing people away when that fails, alternating between people-pleasing doormat and lashing out. She's at increased risk of abuse, nearly three times more likely to be raped than her neurotypical counterparts and getting no safeguarding support as the vulnerable person she is.
Whatever downsides you've imagined because you read some half-baked "labelling theory" from a grant-wasting grifting "social 'sciences'" academic are nothing compared to the downsides to her of not being assessed.