RemoteDesktop: Make fakeinput authentication less hands-on

Moves the handling of the permission to the session class. Makes the authentication be handled implicitly.

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This is an intermetidate step towards https://invent.kde.org/plasma/xdg-desktop-portal-kde/-/tree/work/apol/remotedesktop-auth, which still needs some work. Submitting this separate commit because it addresses an assert when cancelling the dialog.