Japanese monks and emperors kept meticulous records of cherry blossom festivals for 1,200 years. They accidentally built the world's longest climate dataset

https://sh.itjust.works/post/57803561

It’s there a difference in tone or meaning between accidentally and inadvertently? I feel like accidentally means they did something that was a bad thing.
Incidentally would be more accurate perhaps.
I looked up the definitions of incidentally and inadvertently, and inadvertently is a better fit IMO.