I guess extension's privileges means more privileges than a regular web page has (accessing file system for example?), if so then it's even more dramatic.
Right. Extensions have more privileges than normal web pages.
For the specific case here (webextensions), the extension asks for a list of permissions at install time, so which privileges it has, exactly, depends on the extension. https://developer.chrome.com/extensions/declare_permissions has documentation on what the various permissions you can request are.
For the specific case here (webextensions), the extension asks for a list of permissions at install time, so which privileges it has, exactly, depends on the extension. https://developer.chrome.com/extensions/declare_permissions has documentation on what the various permissions you can request are.