Warning: Kind of long post

I've been with this girl for 4 and a half years, known her for 10. The way we acted with each other was always unique. She wasn't my first girlfriend, so it doesn't hurt because of that, but she's the only girl I've ever met that literally did some kind of magic on me, because everything, from her looks to her faults, were perfect for me.

Towards the end of our relationship things were getting messy. We were both living stressful and draining situations, so we couldn't rely so much on each other, we fought, we said bad things to each other (not straight up evil things, just stuff a bit unpleasant to hear). I did stuff I wouldn't do again because I didn't understand why I was doing it. She had problems that was unwilling to take head-on because she was experiencing very stressful situations and suffers from severe anxiety.

The breakup was friendly at the beginning. I know I still loved her, and I don't know if she still loved me, judging by what she said. I gave her some time to think about it, since I was the one that mentioned that maybe we needed to breakup. Three days later, after no contact, I asked her if she came to a conclusion. She said she thought the same thing, so, even if it hurt, I was ready to part ways. But then she said some things that made me not really "friendly". I lashed out at her. She did not expect me to react THAT badly but, as she literally said, it was her fault for not putting enough thought and reason in those words. This was mid-March.

Fast forward to the end of April, after a month and a half of soul-searching and understanding, I realized why I did that stuff. I didn't contact her for that whole time, but when I realized what I did wrong and why, I felt the need to tell her because I owed it to her. So I said hi, talked with her of random stuff for a couple of days to make her comfortable, then I told her what the problem was (and that she was, in part, responsible). She thanked me for that, we both excused for my reaction a month and a half prior, but she did not seem to own up to her mistakes in the relationship. Mostly because, by knowing her at heart and what she said, there was some bad stuff going on in her family (her brother almost died because of the injuries recieved in a bike crash + a lot of very personal stuff ) and she wanted to stay relaxed, without thinking of any problems and/or faults.

We kept talking and things were going kind of good, except a few hiccups, until the end of May, I think it was 25 or 26. The discussion, that day, drifted and, without noticing, I asked her if she would get together with an ex, and other similiar stuff. A lot of stuff became clear: basically, the hiccups were caused by the fact that I was her ex and she still did not get over the breakup. She still saw me as "the guy that just became my ex", and was unable to start from scratch with me. For her, it was still impossible to start from friends or acquaintance level, without caring if we could become something more (ofc I wanted, but I didn't show my game). That hurt me because, in the end, I still loved her. That also made me understand that if we kept going like that I would've been forever locked out of becoming her SO again. So we silently agreed, without saying a word to each other, that I would not talk to her. It was late and the last thing I said to her was "Good night".

Then, when Fallout 76 was announced (May 31st?), she reached out to me, saying that she wanted to break the news of the new game to me (She knows how much I like the series). We talked for 15-20 minutes, but the nice talk was kind of chocked by the situation because, at a certain point, she remembered that we shouldn't talk. (For me it was more of "I need to not talk to her" tho. Maybe she still cares enough to try and get over the breakup to start anew?)

This was the last I heard of her. June 7th is her birthday, and here are my questions...

Should I make her a gift? I was thinking of no, honestly. That may be too much or too awkward, and tbh I don't have the money to waste on a girl that may not want to be with me.

Should I, at least, wish her a happy birthday? This, instead, I think is something I should do. After all, she was the one contacting me about something that we enjoyed a lot together.

What do you people think?

And before you say it: no, I'm not going to chase her indefinitely. I already have a meeting with another girl planned and checking out the rest of the "landscape"