In my opinion propellers aren't part of the engine room.
With the most important reason that most of this part is outside the engine room itself and the only thing u can do on board is checking the lube oil of the propeller shaft if there isn't a leak.
How do the engines/prop working functions tie in to each other?
The crankshaft of the engine is connected to a special hydraulic clutch which then drives the propeller shaft.
depending on the revolutions of the engine (for example a turbine engine) the speed is too big and a special gearbox is installed called a reduction but i don't think the uboats used that because the engines are slow runners.
Also if you noticed when recharging batteries u can see that one engine is in high rpm and one in lower. and in exterior view u can only see one propeller work. The higher rpm is the one of the working propeller which is trying to keep the boat at speed while the other one is connected to the generator that whill recharge the batteries. This is done by that special clutch many ships have. then we call the other engine an auxilary engine.
I do not know if that's an answer to that question but maybe it is a good background information
in my opinion the most fragile part is the propeller shaft because it is long and a very weak spot outside the ship.