Government

Although an emperor nominally rules the empire, they essentially share this duty with the high priest in practice. While there have been times where one or the other is practically a puppet, the strong divide in power bases generally results in each side being a check on the other.
Important to note is that the Eideli church technically does not recognize worship of the Wasp, seemingly backed up by the fact that following it grants no obvious boons. Followers of the Wasp are exceedingly rare, generally kept within families- the imperial line being one of them.
High priests are chosen by the clergy through a convoluted election process.
The position of emperor is commonly believed to be hereditary. Unknown to the populace is the powerful spirit which influences whoever sits on the throne: the Wasp.

Structure

Settlements have mayors. Collections of settlements form provinces, which have governors. The collection of provinces makes up the empire, over which the emperor rules.
governors are expected to supply the empire with one standing legion, which the emperor is free to direct without compensating the province. Additional employed troops may be used as the governor sees fit (requesting reimbursement should the emperor wish to deploy them etc.).
Mayors are mostly expected to maintain order.