it's about context too. Yes, it came out of nowhere but my biggest issue with it is that the only scene that implies a 'romantic interest' from either part is one where she was manipulated by Sybok, and Scotty rejects her because he understands she isn't herself. There is no mutual attraction or romance here. Spock's brother just manipulated her feelings of regrets over focusing too much on a career only and too little on her personal life, and it washed over the first of her friends she interacts with in that moment and she cared about (the writers of the comic interpreted it this way as well). From my perspective, it's like romanticizing the Kirk/Uhura kiss when, actually, both characters did something against their will and for nowadays standards, it wouldn't be that 'progressive' that a white guy is allowed to kiss a black woman only if forced.
Ultimately, as confirmed by Nichelle Nichols herself (in an interview from
here and others), the script, the novelization and even the comics from the time, they were just friends and it wasn't even really intended, by tptb, to get interpreted as romance. I'll concede that while the first scene where she brings him lunch may be ambiguos for characters you aren't used to see being affectionate to each other that way (but then, you are talking about a movie that is almost entirely founded on the 'random' factor), even that one was rationalized by Nichelle as being some sort of homage to her friendship with James, and in particular the concerns she had for his health. [I'll mention that, in the novelization, Uhura's loneliness there is emphasized full force because she had no one to spend her shoreleave with. Scotty heard she wanted to see Scotland alone so he originally proposed to accompany her but then forgot about it and she lost her shuttle]
The only character Uhura shows hints of attraction for while being herself is Spock and THAT'S because they had originally wanted to explore a relationship between them, but those were the 60s and an interracial couple, even if the actor is a Jewish guy playing an alien, was out of question (and I guess by the movies era it was too late and/or still considered too controversial, not to mention that out of the secondary characters marginalized by the Kirk/Spock show, she probably was the most underused especially when they introduced new female characters). Remember the Kirk/Uhura HAD to be forced, and even if forced it was barely, barely (if you read behind the scenes stuff), allowed by the network.