This sounds like a sensor issue. When a Mac is missing data input from a sensor it puts the Mac into a protective state—revs up the fans and clocks the CPU way day. Which is why it takes ages to do anything. It assumes no sensor data means the worst and prepares for that.
Sensor issues are usually related to a handful of spots. It could certainly be the battery, or something that happened as a result of the replacement. First thing I would check is the data cable for the battery. It's the little one that comes off the battery board. It's not unusual for that cable to be loose after a repair. Make sure the cable is fully inserted and the little locking flap is down. This is also not uncommonly an issue with the trackpad, but based on the backstory, I am less likely to think this is the problem.