Ooh. This place would be the king of hydroelectric.
Streets and Walkways raised above the ground, with copious drainage, so they don’t form puddles.
Copious water storage both aboveground and subterranean, starting with massive watertowers that fill when the rain is heavy and are used as low-tech batteries to spin turbines through pure gravity when the rain is light.
Public utilities like street lights being built with water-catchers draining into generators, the lights shining more brightly the heavier the rainfall is.
Every shoe made in the city is designed to have an insane amount of traction, so climbers and naturalists come from around the world to get the best grip. Hell, there’s probably gloves too.
The space under the streets and footpaths funnels into a collection system for a massive system of cisterns under the city, topped with a truly impressive quantity of water turbines for generating power, the flow dropping from one to the next to get as much energy as possible out of each stream before reaching the bottom.
Buildings are built to direct rainwater off in specific directions, and community spaces are sheltered by covers that do the same, so there are breathtaking waterfalls everywhere in the city, many with gardens or power generators or both built in, allowing for falls that take forms you just don’t get from nature, all draining into the generator below the city.
The collection of cisterns has outlets that lead to multiple natural water features like lakes and rivers, and civil engineers carefully control the outflow of the city’s cistern system into each, to ensure they don’t get too much or too little of the stream. If something goes wrong with one outlet, there are many others that can carry the excess between them until the issue is resolved.