In manifest.json it requests the following permissions:

"permissions": [ "tabs", "https://www.googleapis.com/", "identity", "notifications" ]

"tabs" is just needed to check if Kanbanly is already open in another tab. If yes, activate that tab instead of opening a new tab.

The side effect of this permission is that Chrome claims the extensions has access to browsing history (which is incorrect since that would require "history" permission). So it's really a Chrome bug and the WebExtension does not access your history or any content in tabs whatsoever.