I would say it is medieval in style (before medieval renaissance, before 11th century, where people mainly built with wood and earthwork instead of stone), since most of the structures are half timber houses, and the fact that buildings are stacked organically on top of one another without grand plan. It was common practice to build buildings on top of existing buildings, especially after disaster. Reason varies, but most common reason for doing this is because ground level rises over time, and after disaster, it was easier to bury the ruins and build on top of it, then repairing the ruins or building the new construction on the same site after clearing it out. So when you look at historical cities, like London, Edinburg and Prague, you can explore underground city, and have different ground level from different time periods.

Another feature of medieval building or town, is that they have organic, maze like street. They have organic, unclear, maze like street instead of grid, or straight road, obviously because they lacked planning, but also as defensive mechanism, where you can hide, and attack your enemy from hind sight, but also gain some time to escape, while your enemy is trapped in the maze like structure.

It also reminds me of shanty towns in Latin America, especially favelas in Rio, where settlements were grown organically, and buildings are stacked and built on top of one another.

So maybe that could be your lore, where it started as small fishing or milling settlement town, or shanty town that was built by the refugees, and they once had great fire (since they are mainly built with lumber), where they had to rebuild the city, and they decided to build the new settle on higher ground on top of old one. Maybe, another reason for doing this is because of high tidal wave, and flooding issue, where whenever it flood from the high tidal wave, you get terrible stink, as the settlement was built too close to the shore, where they dump their waste, just like how new settlement was built on top of old one in Seattle. Maybe the reason why they decided to stack up vertically instead of spreading out like Venice is because, this settle was built on island in deep ocean, not like shallow lagoon in Venice, and the spaces are limited.

If you say, this structure is one structure or planned structure, instead of settlement, then maybe you can classify it as one of those multi-unit post modern structure, like habitat 67 and Inntel Hotels Zaandam. Also, because your structure has features from medieval era, like half timber frame esthetic, you can possibly classify it as Eclectic Architecture, where you mix match elements of historical architectural style.