Early 2013 MacBook Pro battery issue

Hi, I have a Early 2013 15" retina MacBook Pro (MacBookPro10,1) 2.7GHz i7 16GB RAM running macOS 12.3.1 through open core legacy patcher. The battery has 661 Cycles, that number hasn't changed for a year or so, and says the condition is normal but it dies randomly. Sometimes its around 60% sometimes around 40%. It will go to sleep without warning and when I plug in the charger, it comes back up with around 70% and it can run unplugged until it gets back between 40%-60%. I have reset the PRAM and SMC and neither have helped. in activity monitor it shows around 6 hours remaining on 100% but only lasts around 2 1/2 to 3 hours. It has been doing this for the past couple years since it was running macOS 10.14, and I have just kept it at home on the charger, but now that I am using it for school, its hard when it just dies during class. I have tried to "recalibrate" the battery by charging it to 100% and using it until it dies at 0% but it can never get past 40%. I have also opened It up, cleaned all the dust out and applied new thermal paste, which it has been keeping cool better but that has not affected the battery. I don't know if there is something I need to change or if I just need a new battery, which I hope isn't the case. Any help is appreciated!