To answer your AIBU @OneShyBear - yes, you are being unreasonable to track her down.
But the reason why people are conflating the two issues (tracking her down and the Costa meeting) is because they are inextricably linked to your suspected inability to maintain boundaries in relationships and to understand what it is appropriate.
People make mistakes and bad choices, even wonderful foster carer with plenty of training. Sometimes we have blind spots and it’s helpful for others to point them out. So if you’d come on here, asked the q and then reacted with horror and contrition when people called you out, I think this would be a much more supportive thread.
’OH my gosh, I messed up, I don’t know what came over me, can’t believe I did this, was distracted, feel awful, how can I make this right’
But your doubling down and only engaging with those talking about how to find the woman tells me that you don’t feel like that, and I think the consensus of the comments on this thread is that you ought to feel like that.
I think it’s also worth pointing out why it’s different than tracking someone down in a different scenario. Eg a few years ago, I had a bad car accident, and a wonderful woman stopped to help me and calm me down. I couldn’t remember her second name, just that she was a teacher at the nearby school, so I dropped a nice card in to Jane at An. Other High School to say thanks. I think that’s ok.
But the difference here is that you ought not to have talked to her for so long in the first place. She’s already heard more than she should’ve done about your situation, and you wanting to track her down for further conversations implies that you still can’t see that the interaction was unhelpful.
Best of luck, OP, I hope you can find the support you need to keep your foster children safe and well cared for