It does seem strange that it was her suggestion then she can't be bothered to turn up.

We all like to have a good birthday, I know how it feels if you have a disappointing one. My advice would have been to not contact her about her "no show". It's often better to "play the long game" and wait for her next move. She's not the good friend you thought she was.

We are all different with expectations about friendships. I'll quote a couple of examples from my own. There was a group of us who'd been at the same senior school. Yes, with hindsight, the friendship should have finished then. One escaped a dominant mother by going to uni. Cue outrageous behaviour, failure to contact anyone. She was invited to another's hen night though not the wedding. Again, behaviour unacceptable. Contact stopped with her at that point. The next issue when the married one had first child, remainder of group invited to christening. I went (was a godparent) but other friend used excuse of creosoting garden fence to not attend. End of that friendship.

Am I still friendly with the remaining member of the group, no. She became obnoxious and tried to rule my life as she did with her husband. Final straw was sarcastic comments about my niece. This friendship ended 16 years ago.

Just because she annoyed and hurt you, it's better not to react. As the saying goes "what goes around comes around". Know it's a natural reaction to respond angrily, but you're only sinking to her level.