What's this part good for on my exhaust?

If your previous exhaust had those mixer elbows, you obviously had a wet exhaust - more than likely with a main u/w outlet, plus bypass.
And since a conversion from wet (particularly with u/w outlet, which is the more common) to dry exhaust is akin to brain surgery, it's practically impossible that whoever rebuilt your exhaust did not include somewhere a raw water re-injection of some sort.

This is a cat that can be skinned in several different ways, though.
If you post some pics of your new setup as SeaLion suggested, it should be possible to understand what was done.
But you should show us the whole piping, all the way from the turbo flanges to the hull connection.

Btw, why did you rebuild the whole exhaust?
If your photo of the old mixer elbow is anything to go by, it was in excellent conditions!

The OP said in post #5 that the photo shows his "previous exhaust", and that he now has a completely new one with no mixers.
So, while I would also be curious about the circumstances, only with some photos we have a chance to understand what was done exactly.
In fact, aside from a very unlikely full conversion to dry stack, a new exhaust with no mixers anywhere would be a disaster waiting to happen PDQ!

I'm sorry to say that I don't like what was done in more ways than one.

1) that type of insulation on the (very long!) dry section makes visual inspections of the steel pipe impossible, and I would have asked removable wraps instead. But in fairness, this is a sort of pet peeve of mine, because that method is actually increasingly popular, also among OEM installations.
2) The "Y" connection is made in such way that the exhaust gas have a much shorter and straighter path in the external cylinders bank compared to the internal one, and this is bound to create a difference in backpressure. In this case, I very much doubt that the OEM installation was similar. But if it was, I'd be curious to hear what is the boatbuilder.
3) For the s/steel plug which might be meant for raw injection, aside from agreeing with PacBlue, it looks rather small. Besides, I see no reason for fitting it in a section of the exhaust which looks pretty much horizontal. It would have been much more logical to fit it above the last curve, and pointed downwards, to avoid any potential risk of water reversion at idle.
4) Lastly, I can't see any low rpm bypass, which engine manufacturers always require with u/water exhausts.
Actually, it's possible that the bypass is included downstream of the blue flexible connection, inside the GRP box, but that's something I would want to check.

Anyway, if the engine were rebuilt by a MAN official dealer, they should give you a warranty.
And for the validation of that warranty, they surely want to check and approve the whole exhaust system, both statically and upon seatrial.
There is a specific MAN protocol for that, that they should complete with all the relevant data and hand over to you, duly signed.

I see that you already released the payment, and I appreciate your aim of supporting the company that did the job, of course.
It would have been reasonable to wait the engine dealer approval, though.
At least in principle. On the other hand, in these lockdown days, normal principles are pretty much going out of the window....
All the best for the job completion, anyway.
If nothing else, I would expect that your supplier will appreciate your payment, and remain available for any additional support that the MAN engineer could require.

Nothing wrong in a long dry section per se, but necessary, it definitely isn't.
In my V8 MAN installation (as well as many others that I've seen) the dry section is negligible.
I mean, like 10 inches or so - if that.