We would like to enable a gadget by default on wp.fr, not for everyone but only for non autopatrolled users. Autopatrolled users should enable the gadget in their preferences if they want to use it.

It could be a new option https://www.mediawiki.org/wiki/Extension:Gadgets#Options
"rights make the gadget available (and visible in preferences) only to users who have the specified privileges" but we can't use this.