Check FFG sonar, it works more or less as you described. What screens and systems are used on real subs and ships is not known anyway (I mean not told).
For overlapping sounds there is narrow-band, which means even more math with Fourier transformation. With that you can follow one frequency .. and it should be possible to choose some which does not conflict with anything else.
Again .. how much this is used IRL is hard to tell. From what I read you can assign auto-markers even for BB contacts, especially because they can measure actual rate of bearing, even if the bearing changes too slowly to see it on the screen.
But to auto-follow contacts without being fooled by crossing lines you have to follow concrete NB line I guess.
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