Firstly, if this is a one off incident, it kind of sounds like you want to have found a “gotcha!” moment from your childhood to prove your mother was a bad parent, and this is your only memory of an unpleasant moment to do that?
If this is part of a wider picture, and you don’t wish to share that wider picture (as is your right, your childhood memories and experiences are yours and you’re not obligated to dish them out to any of us), then you must know this incident, on its own with no other examples of your mum’s behaviour, is never going to be judged by strangers the way it is judged by you. The validation you want will be hard to come by when discussing it on a forum like this.
As we don’t have any more examples of bad moments, I’m only going to judge this one incident. It probably was a little bit harsh to snap at a three-year-old but in all honesty, I likely would’ve done the same. Screaming just goes through me, it makes me panic, my head hurts, I tense up, my ears ring; I just need it to stop. If you were just screaming because you couldn’t see her and she ran in and saw that, she was probably just at the end of her tether and wanted you to stop, too. Or maybe she thought you were in serious danger and had that “oh for goodness’s sake!” knee jerk reaction when she realised that wasn’t the case. Also, you tend to have to raise your voice anyway to be heard over screaming.
Yes, children do need reassurance, and to feel like they can express themselves, but parents are human and are allowed boundaries too and sometimes, they don’t respond the best way when their boundaries are (unintentionally) trampled on by their child. It’s part and parcel of the parent/child relationship; it’s never going to be 100% perfect and parents will definitely make mistakes.
You mention your mum being a career woman but felt no need to say your dad was a career man until asked later. Why didn’t your dad’s career choices require “context”? It does seem unfair, to this causal outsider, that your mum’s work choices are being judged while your dad’s aren’t. Again, just judging off this alone with no further insight or examples, it sounds like you have issues with your mother and your relationship, and perhaps you’re unpacking that and trying to seek out more examples of unpleasantness. Whether that’s because you’re weighing up going NC because she’s a terrible parent and this was the beginning of you feeling belittled/upset by her, or you’re in therapy and remembering long buried things, or you’ve had a fall out and want to remind her of her failings, I don’t know.
Memory is a very tricky beast. It’s not always our friend.