Listen OP, her manners aren't quite to the standard of yours.
Does that really matter though? I mean if that's the most important thing then yes drop the friendship - you don't need anyone else's permission to do this..
But where I object is that you are making assumptions based on her actions that are likely not true.
Ok so it was her birthday and she didn't pay a lot of attention to you getting there safely. She may have been stressed getting the party organised. I was on my last one, everything was going wrong. I didn't have bandwidth for checking up on people individually. They all managed to get there.
The wedding present - just because you would have sent thank you cards doesn't mean that she's great at that sort of thing. She did acknowledge your generous gift and hopefully when they go they will send you a photo and thank you properly. That's what I would do and that's what I've received from people too.
This doesn't mean you're the filler friend. Or maybe you are but not in a nasty way. Perhaps she has a big circle and you're not part of the inner circle. That can feel hurtful but it doesn't mean ill intent. It's just different sorts of people. Perhaps she has a different attitude to friends - my partner definitely does. He's not a bad person, he likes his friends but he doesn't get very attached, he's more family oriented.
My final point. From your posts, you are coming across like someone who wants to be right on this matter, to prove she's a bad person / friend and you're good. You're looking to be offended. It's really tiring to be on the receiving end of that. Don't be surprised if she steps away from you rather than the other way around.