Also had no idea but browsers do seem to leak their incognito state:

https://stackoverflow.com/questions/2909367/can-you-determin...

Just a small notice that Big Brother is disappointed in you :)

I wonder how do they detect it, maybe there is no LocalStorage on incognito mode, but TBH it should not be visible to a webpage

"Chrome's FileSystem API is disabled in Incognito Mode to avoid leaving traces of activity on someone's device. Sites can check for the availability of the FileSystem API and, if they receive an error message, determine that a private session is occurring and give the user a different experience."

That’s one way, but they would have had to have used multiple solutions depending on the browser.