One of the planets in my book series is Aurea, a very populous planet with about end-of-the-middle-ages technology (cannons galore but still haven't really figured out arquebuses or muskets). Aurea is a very culturally diverse world, although most of the provinces have cultures most similar to Roman, Byzantine, and Ancient Greek cultures with a hint of al-Andalus and the Wild West. The three exceptions are Tangolia (various Hunnic, Turkic, Mongol, Manchu, Navajo, and Comanche-inspired steppe tribes in the vast deserts, steppes, and mountains; while the coastal urban population is more Korean and Chinese-inspired), Tiorangi (A fusion of Maori and Aboriginal Australian-inspired tribes and the wider Greco-Roman culture of Aurea), and Zebusylvania (Imagine Zulus and Zandes that have absorbed a great deal of Greco-Roman culture). Of the three, Tiorangi is the most assimilated into mainstream Aurean culture, Zebusylvania is somewhere in the middle, and Tangolians barely consider themselves Aureans at all. All three are descended from successive waves of migration into the parts of Aurea that the mainstream Aureans (called Guants) left empty, and all three have histories of both trading and violent wars with the Guants until they were eventually subjugated.
In order to hold onto such a diverse population, Aurea's government long ago split it into 8 provinces: the three mentioned above, Argentolia (home to the capital of Astras and over a third of the population), Centronesia, Terra Centralis, Thoronodos, and Occidens. Each province (except Argentolia) is allowed to have its own system of government, as long as they have a single leader, abide by all federal laws, allow the Aurean Government to collect taxes, provide troops for and lead the portions of the military under their command, and abide by all of Aurea's foreign policy decisions. Most of these provincial leaders cooperate with the Aurean Government without issue, but the Zebusylvanian Kings and especially Tangolian Khans have betrayed the Empire on multiple occasions and directed their armies at the Aurean Government, although none of these uprisings have been successful.
As I said above, I've figured out how the "federation" aspect of the Aurean Government works, but I'm having issues for the rest. I want the planet to have a strong Emperor figure who acts as the superior to all of the seven provincial leaders, is hereditary, and has either absolute power or close to it, but I also want there to be some sort of American or Roman Republic-style elections planetwide that actually matter (although the various aristocrats have a disproportionate but not total say in the process), and I don't really know how to make these both true at the same time. How do I make an overarching government at least mostly Republican with planetwide elections whose stakes matter, but also have an emperor figure with close to absolute power as well as the decentralized province system outlined above?