Are Chrome and Edge tracking what you do even outside their own context, like hard drive and memory content?

Most of my Chrome usage involves using the Google ecosystem anyway (Gmail, Youtube, Search and the like), and within Edge I use the Microsoft ecosystem (Azure, OneDrive and similar), so I guess I'd be tracked exactly the same way even if I used another browser on both.

Is that true?

azure chrome context drive ecosystem edge gmail google hard hard drive memory microsoft onedrive own privacy search tracking youtube