This might be technically impossible, but maybe not: The desktop app timout “on system idle” is very handy, however, there’s no similar setting e.g. for the Firefox extension. Would it be possible to add a “on desktop app lock” timeout to the browser extension?
Sidenote: I changed the title from “Browser extension timeout in sync with app” to “Browser extension timeout in sync with the desktop app”, to make it more clear what this Feature Request is about.