The AIS plot shown above is very strongly indicative of the search vessel looking at a credible search datum.
They are clearly using Dynamic Positioning (DP) to manoeuvre the vessel on the search pattern and they are clearly using a deep tow sensor. They are not 'towing' the side-scan towfish or deep-tow pinger locator like a trawler tows a net. It's not astern of them, most of the time.
Sidescan sonar seems quite likely, but you would use a very similar pattern to 'box in' a suspected target with a deep tow hydrophone to locate a pinger signal.
A sensible searcher would concentrate his efforts, at this stage in time, to getting best data from the battery-limited pinger.
The way you do that is not by triangulation but by measuring the signal strength as you pass by the source. You plot that out with signal strength in the Y axis and the distance along track on the X axis. You get a parabolic curve, albeit a lumpy bumpy one which can sometimes be a bitch to interpolate. Maximum strength suggests that that is where your line reached closest point of approach (CPA). That gives you an LoP to/from the target, perpendicularly. By repeating that line perpendicularly you get a cross-cut of that LoP. By covering the other two sides you eliminate the baseline side confusion and further refine the position. Voila. You have a good approximation to the actual co-ords of your Dukane (or whatever) pinger.
I do, however, concur with those who have pointed out that the line-spacing is more consonant with a medium frequency sonar run, eg 125kHz, than what you would choose for a broad-brush pinger locator run in anything other than very shallow water. The reason why I think it's more likely to be a pinger locator on the end of the wire than a side-scan is that the speed over the ground is something like half a knot. That's Okay for a hydrophone but would not be enough water speed to keep a side-scan towfish on any kind of of sensible heading and would make sonar trace interpretation impossible.
I therefore conclude that they've got a pinger within earshot and are boxing it in before putting an ROV onto it.
The water depth at that locus, btw, is approx 3106m. The seabed sediment consistency in that area is like baby-poop. ROVs will have to be negatively ballasted, ie positively buoyant at bottom depths, so that they don't stir up the fluffy sediment and blind themselves during recovery of high value items such as the 'box(es)'.