Hi
I will find the passion in the book "Das Boot" and I will try to introduce a complete explanation of the problem here.
Just in a nutshell it's the way you wrote. If the ship goes into ever-greater depths, the weight of the water column is constantly increasing, and the ship continually compresses and thus increases its weight. The air that is in the submarine is constantly compressed, and so the less and less the boat is hovering. And at a certain depth, the ship gets to the condition that it is no longer hovering, but it falls naturally. And there are two ways to lift the boat, either use compressed air and inflate into ballast tanks, increasing air volume and active buoyancy, or using engines and rudders.
Just like a submarine captain you have to be able to decide what depths you dive into and how to use compressed air.
