So I'm working on a fantasy strategy game where I wanted to do a lot of river based content.

The maps are procedurally generated. Below I've copied some text from a post about this issue:

Axioms is a fantasy game and as such the default map generator isn’t configured to generate a world quite like our own. Instead at the high end it generates a world roughly 10x the side of ours and it is roughly 70% land. Half the water area will be oceans, so 15%. Given a size increase of 10x for the overall surface area that means 1.5x as much square mileage.

12% of the world will consist of inner seas like the Baltic and gulfs like the one in Mexico. The Mediterranean Sea is roughly 0.5% of the surface of the world. That is roughly a third of the non-ocean salt water in the world. So those areas will cover roughly 8x as much surface area as they do here.

That leaves 3% of the surface area of the world for medium to large lakes, inland seas, and navigable rivers. This is 3x the percentage of our world that is fresh water. Which means it is 30x as much surface area covered in enclosed fresh water compared to our own.

The main purpose of this change is to reduce low quality space which limits the scale and complexity of civilizations. More great rivers, ideally in complex connected networks, more lakes, and more inner seas allows the world to open up proportionally.

There is far less wasted deep ocean. In a lot of cases the reduction in ocean market share just means sticking a big continent in the middle or having a vast and varied archipelago. For my purposes a bunch of empty ocean is low value. There is also a lot more valuable land proportionally which means more variety in states.

My question is specifically about navigable rivers. About how deep/wide generally would these rivers need to be? Is there any sort of river/heightmap algorithm that is commonly used that I can modify for map generation? Since the game uses a "province" system and not a hex or square system I don't need to get super fancy. If as noted in the post I want pretty expansive river networks compared to Earth is there anything special I can do with the heightmap to encourage that in a natural looking way? Of course as it is a fantasy game I can pretty easily do some "gods did it" stuff to fiddle heightmaps around.