> But apart from AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering?

Nothing, really. This mirrors other examples of blowups from the classical physics. It's possible to create a system with just gravitating bodies that exhibits a blowup to infinite speeds in a finite time. The root cause is that, in classical physics, the speed of gravity is instant.

In the case of Navier-Stokes, the fluid is incompressible. So technically any force that you apply to it is supposed to instantly affect everything else. This can be exploited to create these blowups. In reality, no fluid is incompressible, and it takes time for any action to affect the material.

It's just that Navier-Stokes equations are so slippery that it's hard to pin their behavior down. They basically just restate the momentum conservation law for a continuous medium.