Need online dating advice
Backstory: A few months back I met this amazing girl through social media. We started talking to each other, and at the beginning I felt like everything was going well, she was showing interest, we were talking consistently etc. We live in the same country but a few hours away from each other. The problem comes when I acted stupid and moved too fast. After that, the conversations started to get slower and drier, to the point where we went no contact. Looking back at things I understand her and understand that may have put pressure on her due to the facts that we met online, distance, etc.
She lives in a big city where I have never been and always wanted to visit. I had told her that I wanted to go before things became awkward. I planned the trip and went there (I didn't go specifically for her but meeting her would have been the cherry on top of the cake. I broke no contact to tell her I was going there and when I was there I messaged her again to meet, but she told me she wasn't specifically in town and she was busy, so she couldn't make it. I told her that if she ended up coming in town to let me know, she replied saying okay and that is the last message in our chat. I left it unopened because at the time I thought it wasn't worth it. We haven't talked to each other since (which was a couple of months ago).
Of course I was sad about how things went, but it was not a heartbreak since our "situationship" or whatever you may call it never got further than talking.
Now the advice part. In a few days it will be her birthday. I don't know whether it is worth it to wish her a happy birthday or not. The way I see it is that it is a humane gesture of saying hey, I wish you a happy birthday and I hope you are doing well (of course the message would not be like that but that would be the meaning behind it) with no expectations back. On the other hand I don't want to pressure her again. Maybe she would want to see my message, maybe she would feel awkward about it. Whatever I decide to do feels like will be the wrong decision. I thought that the most conservative choice would be that instead of directly messaging her, in case she posts about it, I would reply back with the happy birthday message. If she doesn't, I won't say anything. But I'm quite stuck in this loop. What should I do?