It's one of the objective in the long run but it does require a lot of work to get everyone on the same page.
I am currently working on implementing the "Système de Design de l'État" for a french governement service but unfortunately it is still pretty chaotic right now since there are many modifications of components with breaking-changes / no backwards compatibility with almost every releases.
Don't worry, I know it's not that easy, and good for you for sticking to the design system rules! My sarcasm was mostly directed to the chaos introduced in state services by giant consulting firms doing there own thing quick and dirty...
Yeah, in theory the French government offers a ton of super-useful APIs to its services (to automatically fetch paperwork for a procedure, for instance) but the big services use almost none of them.