I've been doing some reading about the Crusades and about Venice's rivalry with Genoa, and it seems like the way they thought about Saints seems like polytheistic worship, and how city states in ancient Greece or Mesopotamia would have a patron deity. The most striking to me was how Venice would raise its banner for Saint Mark, and Genoa for Saint George, and going to war as if they were representing different gods.
How "polytheistic" is medieval Catholicism in the Mediterranean compared to today or the early Church?
Exactly, no, Saints were more like patreons or icons that represented cities, provinces, territories, nations, etc. Saints gained their sainthood throught actions that the church considered important, either being by theological additions (like Saint Agustine of Hippo, Saint Thomas of Aquino, etc), martyrdom (Saint Sebastian, Saint George, etc), or other things. Nations that would have a close relaiton with the church, pope or the patriarch (in case the nation followed another church) would often get granted the representation of a saint to as a way to show the importance of the nation to christiendom, which of course, this included flags (but every now and then there would be exceptions, like embracing the flag of a crusading order like did the county/duchy of Savoy or the kingdom of Prussia taking their flags from the Hospitaller Order and Teutonic Order respectively). Many of the most iconic saints come from the days of the early church, many of them are only martyrs during the roman persecutions, but they're not workshipped as gods, I would dare to say they're more on the same ground as national heroes, iconic and influential monarchs, and characters of the same caliber.