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.
Well, yeah, I guess we will have to agree to disagree. I certainly don't think we need an outright confirmation of autism itself (though I don't really know what other spectrum she could be referring to) to interpret actions as being a result of inferred autism. In fact, if there's one thing we do know, it's that things being out of place drives her insane. In the comic, when giving the briefing, she notices that one of the portraits is askew and she can't see how the others can tolerate that. That reeks of heavy implication to me. But either way, you don't need to be 100% sure of something to be able to able to interpret a gesture as meaningfully indicating that thing.
And about her being incapable of negociating, that's simply wrong. Social skills aren't just a monolithic set of skills that if you have in one circumstance, you have them in all things. To negotiate a business deal, especially in the formal environment of an office as opposed to a resturant or bar as some business people go to, you don't need a keen awareness of humor, which I might remind you is what we were originally discussing. You need to be able to work out the best deal, possibly the best compromise, know when to press on an issue, know when to fall back, etc. Like you pointed out, she doesn't know where on the spectrum she falls, which means she could easily be highly competent in formal settings while absolutely clueless in informal ones. A lot of people who have social difficulties are able to compensate or learn them in other ways. Hell, one example is that even though the askewed portrait bothers the shit out of her, she knows it would be inappropriate to draw attention to it. So your arrgument that her autism immediately invalidates her ability to navigate social situations simply isn't correct.
Order, perfection and harmony are among Symmetra's core beliefs and values. Yes, it is not a laughing matter to her that the camera in her highlight intro is crooked, but it is still presented in an amusing way. If we weren't supposed to find it amusing, then Blizzard wouldn't have included it.
Oh, I don't disagree that it was meant to amuse, but my point was that that was not her being funny as an expression of her own sense of humor. She's still "Serious", she was just put in a funny situation. Which, again, can be the same thing with Hanzo's pokemon line.