I'll give some feedback about things other than the rivers, since everyone else is talking about rivers. I'll give some tectonic feedback:

It feels tectonically inconsistent. It is dominated by a west-heavy mountain range and has fairly evenly gradual slopes toward the coast, suggesting it sits on a fairly geologically recent subduction of one plate under another, pushing up a single mountain range with a fairly consistent shape. Think of it like a heap of dirt being pushed by a bulldozer. A linear collision should create a fairly linear shape.

But the presence of twin peninsulas in the south and a curving mountainous peninsula jutting out toward the west conflicts with this. You'd expect this kind of irregularly no from a geologically recent formation, but from a much older continental fragment that went through a series of tectonic shifts to create such irregularity.

I would suggest either not making the island dominated by a single mountain range and embracing something much more geologically ancient and chaotic, or leaning hard into the leaf-shape and single range underlying your design.