My laptop died and wouldn’t boot up without dying.

I was on my Mac the battery percentage was at around 90 ish and 512 cycles when it suddenly turned off. I tried turning it back on but it was dead. Plugging it in, the MagSafe charger was amber so I let it charge for half an hour. Half an hour later, the laptop boots up to around halfway then shuts off immediately after. It repeats itself for 3 times then shuts off. I decided to go to bed after that and left plugged in all night. When I came to turn the laptop on in the morning, I got a dead battery indicator. So I left it to charge for an additional 7 hours and when I came back it booted up normally. After booting up normally, I noticed that the battery indicator was gone and in system report it showed that the battery was disconnected. So I opened my laptop up and I saw that right side of the battery was swollen. My new battery is coming sometime this week but is my issue a battery issue or something else?