I would expect a war ship to not even have doors between compartments - only move between compartments at the end of shift, by climbing stairs above the section wall and descend on the other side.

The deepest compartments (below the waterline) are often like this. It is not always possible for taller equipment spaces (engineering, magazines) in small ships. Crew berthing is often below the waterline and accessed via deck hatches as you say, but you do end up with hard choices when the space is flooding and people are still unaccounted for. Hope you can stabilize the ship or run it aground before it sinks, or 100% guarantee that some crew will drown?

Above the waterline, it is common to have “loops” of passageways for movement of equipment and people (including casualties). Firemain stations will be spaced along such a loop because they are used to both fight nearby fires and dewater the compartments below.