but the language of "your computer" implies files on your computer, as it would be what people commonly call it. Merely just the extension is not enough.

If it has the ability to scan your bookmarks, or visited site history, that would lend more credence to using the term "computer".

The title ought to have said "linkedIn illegally scans your browser", and that would make clear what is being done without being sensationalist.

And I spend a lot of my time at home on my computer. The article should have said LinkedIn is searching my house.

It looks like it's also gathering info on your OS and graphics card which seems very much "your computer"

This is just the next iteration of the issues with Linux file permissions, where the original threat model was “the computer is used by many users who need protection from each other”, and which no longer makes much sense in a world of “the computer is used by one or more users who need protection from each other and also from the huge amounts of potentially malicious remote code they constantly execute”.