That's not projection. That's a screw-up and I'm sorry your T deflected it like that. Thing is, some of your feelings will be projection, and some won't, and you're experiencing them as being in the here and now - so it's at best unhelpful, and at worst utterly anguish-inducing, to be fobbed off like that.

Can I ask if it's possible for you to try a different T? I'm wondering if this one has quite a 'blank slate' philosophy, whereas some Ts bring more of their real selves into the room and own things when they make mistakes. It's all very well having firm boundaries but saying you'll do something and not doing it is a real mistake and I think it's invalidating to say you're projecting - maybe this T's approach just isn't right for you.

I'm really sorry as it sounds like you have enough to worry about already. I suggest having one conversation with your T about how you feel and pointing out that while it may be triggering older feelings, it's not solely projection as something had to happen (the T making mistakes) for that projection / triggering to occur!