The US were republics with democratic elements, and a limited franchise,
from 1776 on. The confederation was strengthened in 1789, in that
there was representation directly elected to serve in the national
capital (House of Representatives), in addition to deputies of the
state governments (Senators.) The latter have been directly elected
for over 100 years. This slid our "compound republic" a little further
down the continuum to "direct democracy" than it had been. Other
reforms introduced in the "progressive era" were the initiative* and
referendum,** in the various states, though not at the Federal level.
Interstellar federations where communications are no faster
than ship travel, and even FTL travel takes significant time,
lends itself to arrangements similar to far-flung colonies on
Earth prior to the telegraph and radio. Once you introduce
"subspace radio," an ansible or the like, and the center can give
the periphery orders in real-time, or a trans-galactic assembly
can convene in a virtual space, then less distributed arrangements
can make sense. We could have the latter now, but while business
makes frequent use of teleconferencing and online document sharing,
representative government sticks with in-person interaction,
for the most part.
If both transportation and communications are FTL, and trekking
to Altair VI and back is like flying from London to Wellington,
a unified or closely federated polity is possible.
What makes me wonder is; why be connected? For trade? What
would Sufficiently Advanced Humans trade for across interstellar
distances that would have to be physically moved? Encrypted
information that couldn't be entrusted to transmittable form?
Actual humans with unique skills or knowledge not committed
to some media? DNA in the form of sperm and eggs to increase
genetic diversity on colony worlds or habitats? This is why
we have had "thionite," "spice" and "dilithium crystals"
as goods that are in high demand but only available in some
particular environments.
*
https://en.wikipedia.org/wiki/Initiative
**
https://en.wikipedia.org/wiki/Referendum
Kevin R