Well... it depends. Managing to find a sub 50km away is not realistic (1vs1 scenario) most if the time. Maybe if you can find it with ka-27 but then it has its own torpedo to engage it.
When would you ever send a single ship to hunt for submarines?
Sea bed sonar arrays around Russian naval bases together with land based aircraft including MPAs as well as quite a range of ships will be part of the search, and any ship big enough to carry the UKSK vertical launch system that these ballistic rockets are launched from will also carry helicopters.
If a corvette is operating a helicopter that is searching the water around where the corvette is, why burden the helicopter with half a ton of torpedo when it can carry extra fuel and stay out longer and use more sonobuoys to find the sub?
The helicopter doesn't need to carry torpedoes, the ship can launch them easily enough.
Also, firing a torpedo is quite loud depending how they are launch. It can be detected by enemy sub if close enough. New ones fill the tube with water and turn on their engine so quite stealthy for that regard.
The older systems would be being phased out... the current standard would be the light Medvedka and the heavier Ovtet which are both vertically launched from ships... I rather doubt a sub would notice a launch, but even if they did what does that tell them?
A circle 50+km around that ship there could be any number of targets they might be launching something to attack... its first warning it is under attack will be a torpedo splashing into the water perhaps 1km away... maybe much less...
Same for the system in your video. It turns on its rocket engine in the water making huge noise that will be heard by any sornar hundreds km away.
So you are in a sub and 100km away you detect a rocket motor briefly fired under water... what do you do?
You have no idea it is coming for you... do you run, do you hide... no point releasing decoys and jamming yet... 3 minutes later there is a splash 500m in front of you and a torpedo turns on its active sonar and accelerates to 50 knots and is heading in your direction... no time to dodge it.
Finally for your last point, such torpedo are designed to splash the water, free fall in spiral and look for the target.
IF it lands close enough the sonar on the torpedo will be able to detect the sub without having to resort to active sonar...
Plus if you are lucky it might be a torpedo... in WWIII it might just be a nuclear depth charge to clear the area.
So how do they decide whether to engage the enemy submarine with the Otvet or the 91R and 91ER?
They all essentially use the same mini torpedo, the difference is the rocket booster that takes the torpedo to the target area... if they have 91R in their torpedo tubes they might not have any Ovtet in their UKSK launch tubes.
As far as the target is concerned it wont care what delivered that torpedo.