The basic ones would be

Provide justice

Protect citizens against violent aggressors

Ensure the respect of the law

Run a coherent administration

Levy taxes to fund the above

https://en.wikipedia.org/wiki/Royal_prerogative?wprov=sfla1

Regal functions in my mind are the last ones that will be decentralised. I doubt that they ever will be distributed.

All the rest could be handled by protocols with sufficient coherent coordination.