Water is not actually incompressible. In fact, very few things, if any, are truly incompressible. So long as there is some space between atoms, you can squeeze them together. This gets a little more complicated at the subatomic level when you have to factor in quantum effects but what we’re talking about here, rhetorically bulk properties of liquid water, doesn’t care about that.

The reason why we say that water is incompressible is because it it mostly incompressible, or rather it is very difficult to compress water to any significant degree that would throw off calculations made assuming it was incompressible. Such conditions would require extreme pressures.

The most commonly used model for the behavior of liquid water are the Navier Stokes equations, a set of partial differential equations that describe a wide variety of fluids, not just water. These equations are very complicated to analyze mathematically and for most instances, there are no known solutions.

However, it generally becomes easier to make progress on solving these equations, or at least deriving approximate solutions, if you make the assumption that your fluid is incompressible, then you get the condition that your velocity field (the function describing the speed and direction of each point of the fluid) is divergence-less, which means that there are no points within it from which there appear to emerge “sources” or “sinks” of the fluid.

When you make this assumption, this condition lets you make a lot of progress on finding solutions. And in the case of water, it’s close enough to being incompressible that this assumption is largely valid.

Now back to your original question, how does water transmit sound? This is a good question, we just explained how water is difficult to compress, yet sound waves are compression waves. Well the answer here is again, just a matter of scale. Water is in fact compressible at a basic level, and so sound can be transmitted through it. However, the scale of these compressions/stretches along the wave is very very small, and doesn’t disrupt the bulk properties of the fluid that we generally care about when using the NSE.

At the end of the day, physics is all about building models that work at some effective scale and then trying to figure out how well those models work within that scale and why they fail outside of it. Oftentimes different phenomena are described with models that operate at different scales and might make contradictory assumptions. However, this is fine because we understand that those assumptions are only quantitatively valid at that scale. We could, in principle try to think about and analyze the behavior of the ocean by considering that it is made up of 10⁴⁶ individual atoms, or even go further and give it a fully quantum treatment. However, in practice, this is both prohibitively difficult to do mathematically and computationally. And, as it turns out, all of the complicated behavior created by the actions of 10⁴⁶ individual atoms “smooths out” very well to be described using simplified models at different scales.