As far as I know Slava too has such a variable Depth Sonar. Practically they put a crane outside to recover the thing, however at one point the fish comes just below the ship by pulling it in, and during that phase I think the hollow section helps by either channeling the water or just by slowly scraping the fish to the middle of the stern where the crane can catch it. As for the boats, I'm not sure about that, I'll check on it too. I also have pics of Ropucha's who have shrouded props, but the props are also brought up in hal circular tunnels in the hull (obviously to reduce the draught) yet again tunneling stuff in the hulls... They seemed to have liked such things
As for the extensions on Udaloy, check again my (now updated) topic on that ship. You'll see the shape of these extensions on an Udaloy. Practically it has big bulbs on the outside and much smaller ones on the inside. In between there is a ridge connecting the bulbs and, as speculated here, creating a half duct on the upper side of the prop. The reason for the smaller bulb on the inside seems to be the need for steering.
One rudder and two props is already a disaster for steering a ship, as the rudder only comes in the slipstream of the prop when it has already a considerable degree off centre. When you have two rudders, one straight behind the prop, it's immediately in the slipstream and hence a small deviation from the rudder will already create some steering force. (less rudder angle, more speed).
So practically I think by using these bulbs they either just improve the propulsion efficiency for the props, reducing noise by reducing the cavitation, or they improve propulsion and steering. The fact that on later Udaloys the feature can still be seen, might, as SSN suggests, mean that it's an effective solution...
(another small note on this, the bulbs might have had, as a main purpose, improvement of propulsion and reduction of noise, while possibly the smaller bulb is only there to MAINTAIN steering rather than really improve it. Possibly steering got worse when they used a big bulb on each side and hence reduction of the inner bulb might have brought them back to normal steering capabilities).