OP this sounds very stressful for you. I doubt the teacher meant to snap at you - teachers have that “voice of authority” thing, and if you are making a complaint against your dc’s class teacher then you can expect it to be quite formal, especially if you then complain that the teacher lied to the HT when the incident was investigated.
Honestly in this situation, I think you have to let it go. You are building up a huge construct in your mind, and you sound paranoid , you seem to be working this up into a huge thing … for what purpose?
Think about what the teacher is trying to achieve: a calm end-of-school-day for your dc. That’s all. She has no hidden agenda, I promise you. You are part of a busy, complicated school family now. The staff will have the dc best interests in their hearts.
If you are arriving at the playground in a state of high anxiety, is this ramping up your dc’s negative response? The teacher didn’t just come out with the comment out of the blue, there must be some context … what came before the comment? Sounds like teacher is worried.
You caught the teacher at the end of a busy day, when she has a dozen other parents’ emails and requests to deal with and at least several hours of work to complete - and you start telling her about your MH problems - it’s not the right time or place. That isn’t a classroom exit conversation.