this is such an interesting thread for me as I have the exact same problem as the OP. I am an extrovert and I genuinely try and tone it down at work as I honestly would hate to offend people or get in their faces with my chatter and small-talk.
BUT I work in a creative industry (TV) and so much of my work is within a team, that we do need to communicate. And i have a colleague (sits next to me) who is silent to the point of rudeness, so much so that she will only bark out monosyllabic answers to work queries, and looks at me with a face of thunder.
I have to go elsewhere in the building to get my conversation fix, that's absolutely fine, and I've stopped attempting small-talk with her as I get that she hates it. But I do find her rude, and hard work, because she kind of makes me feel like an imbecile for even attempting any kind of communication with her. She's so condescending and snippy.
And she never ever asks me a thing - recently went on holiday and not a word from her on my return. She has reduced me to tears on occasion (I've run to the loos) because she can be just so unpleasant.
I've tried occasionally emailing her to check she's ok, as I know she has suffered from depression, but I'm really conscious of not invading her space. She's said 'yes. why?' in response, which shuts dialogue down.
I don't want to be her friend - I couldn't give a toss about cultivating a fake friendship, and we're totally different, but I do prefer to work in a pleasant environment. And her negative moods hang in the air like a black cloud.
But I try not to take it personally. I'm sorry for the essay, it's just that it's happening RIGHT NOW and the OP totally resonated with me. It might be hard for introverts to believe, but extroverts don't always have it easy either, especially when the people around them are giving nothing away. I probably wear my heart on my sleeve too much.