It's not really hinted at, it's an insanely mild implication that is heavily left to the reader's interpretation.
She says that she never really felt that she belonged, and always wondered where she was on the spectrum. This might or might not indicate the autistic spectrum, as some people have interpreted. The writer might've meant something entirely different when saying this, or specifically chose that wording to let people speculate about what exactly she means.
Given the fact that we don't know whether Symmetra really is an autist or not, it also is impossible to infer that her sitting down on a chair or being annoyed with a crooked camera angle is supposed to be a representation of her lack of interpreting social cues (especially since in regards to the chair emote, all the other characters are getting a sitting emote as well - her just has the added exaggeration of creating a chair out of thin air to sit on), or her being unaware of how it might be perceived by others. In fact, I'd argue that you're flat out wrong with that particular interpretation simply because if she really did have problems with social interaction, then her employer company Vishkar would not send her to represent the company and strike a deal that is mentioned numerous times to be quite important to Vishkar (to the point of them committing industrial espionage and sabotage to acquire that deal), but rather send somebody else who is more capable of handling business talks, especially ones that require negotiating skills and social finesse.