Thank you for the great detail! The state that you work in when you work remotely depends on whether your location is based on their convenience or yours. In other words, if the office was in MA, but they "let you" work in NJ, then you worked in MA. The headquarters of the company doesn't matter as much as where your office base was.
Since you lived in NJ, they either a/ had an office for you in MA (whether you opted to go there or not) or b/ didn't want to register with NJ for having an employee there or c/ made a total mistake.
I couldn't tell you whether you should have paid taxes to MA without understanding their logic more. Did you ask them why they withheld for MA? You should.
Either way, you have a part year resident return with NJ. You also need to file a nonresident return with MA if its because of an available office.
But why all of a sudden allow you to work from home in Florida? (the fact that they didn't withhold taxes means they are now treating you as working from home). Did you work for the same company?
Based on your Florida W2, you worked in Florida and lived in Florida. So that would be "easy" if correct.
