When discussing compressibility, we are really wondering how much the material will push back if we forcefully shrink it by a certain amount. Think about a very loose spring. You can forcefully shrink it by a huge amount, before the force it exerts back becomes large. A very strong spring only needs to be shrunk by a tiny amount before the force it exerts becomes large.
Water is like a really strong spring. You can make it a tiny bit smaller with a huge press, but the force it exerts back (and hence the force your press needs to exert on the water) increases extremely quickly. Therefore, it cannot be shrunk by much by most presses (though for instance, if you threw it into a neutron star it’d definitely get strunk).
A strong spring can still transfer information in the form of vibrations, it’s parts just don’t need to be expanded/shrunk by very much to do so in the process. The same holds for water.
EDIT: If my math is correct, the a kilogramme of water at the bottom of the mariana trench will be a few % (4% or so) smaller than at sea level, due to the immense pressure there.
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