The "trajectory of the empire" is that it became the Roman Catholic Church. Rome still rules a sizable portion of the world's population.

I wonder if the USA is going the same way. Democratic Church of America?

Not to wade too far into weeds, but the spiritual and temporal authority of Rome (ie what is now called Church and State) were considered separate entities. When the temporal authority collapsed, the spiritual authority preserved its content and form and then simply waited for conditions to improve.

Τhus the various attempts to re-manifest a Holy Roman Empire in Europe across the subsequent centuries.

Rules? Membership of an organisation is nothing like being a subject of an empire. Its purely voluntary. It has less power over its members than employers do. It cannot tax, only ask for donations. Its not even Rome - its run by people from all over the world. It controls only a tiny bit of territory.

Homelander approves.