Is it bad for me to want to slowly drift from a friend who forgot my birthday?

So for some context, I just turned 18. This firmed of mine, who I’ve been friends with for 5 years forgot to wish me happy birthday. We’re in different schools and have different schedules so we haven’t really been texting often and the last time we met each other was 6 months ago. On my birthday, I was really just waiting for my friends from my previous school to wish me because we have all inevitably drifted apart. She wished me on the next day and when I told her my birthday was over, she said she was too busy and didn’t realise the date, then she said she would post an ig story for my birthday. I honestly didn’t need it and was just disappointed she didn’t wish me on the day itself. Then the next day comes and she texts me again, she said she was wondering why I didn’t repost her story but she didn’t realise she didn’t even post it. And at this point, it just feels like she forgot about my birthday and was just trying to find excuses(?). I texted her a paragraph letting her know how I was disappointed and how it felt like she just forgot. But all she replied was a picture with my birthday on her calendar and saying she didn’t forget, which I feel didn’t address any of what I mentioned to her. I also mentioned I would like to be in contact more often as we haven’t texted in like 6 months, and she agreed but when I texted her again, it took her a month to reply. This is something I genuinely don’t understand because how busy can you be to not have even have a minute to answer my text. When she replied she said she was busy with exams and gave herself one week to relax before replying to everyone. Right now I just feel like we’re not very compatible because I get disappointed every time she takes so long to reply me despite it happening multiple times already. What would you do in my situation? (I genuinely would like to get some advice as I’m at a total lost of wondering if I should initiate first again or wait for her to text first)