I have to agree with PP that there is a fine line here.
Your thinking seems a bit 'black and white' on this issue.
The average person we might work with, as an example, doesn't want or need to know about your trauma or mental health issues unless it's very relevant to the conversation. So yes, they do want you to say you're fine (and to seek support from a more appropriate person, not them).
Not because they expect you not to have emotions or to actually be fine all the time but because, as adults, we all need to direct our needs for support to appropriate people.
Think about it the other way around - many of your colleagues will also have trauma in their backgrounds.
You go in on Monday in a mental place that's not great...you ask Carol from Accounts how she is and she tells you she isn't feeling great and tells you all about her childhood abuse at the hands of her father and how that's impacting her...
After that, you get to the staff kitchen and pop the kettle on and Emma is in there. She's in floods of tears over a relationship breakdown at the weekend and tells you all about it and how it's triggered her fear of abandonment from her absent father.
You finally sit at your desk and the colleague next to you starts talking about their anxiety due to their current debt problems and how they have an issue with overspending because they were bullied for being poor and how their mother had untreated bipolar disorder and became a hoarder and that she was too embarrassed to have friends over and that she's never got over the feeling of being judged and so now spends money she doesn't have trying to look polished and put together.
How is your own mental health doing now?
The sad truth is that many of us have all sorts of trauma in our backgrounds and we need to have boundaries in place to function as a society.
Oversharing is a symptom of trauma and it feels like you'd like to overshare more than people not caring.
(I say all of this as someone with a traumatic childhood who has also had to work through an occasional tendency to over share).