This is book 14 of the "Aubrey-Maturin" series.

This note contains spoilers for the book.

The title comes from a second ship they're given, a Dutch warship that was deliberately sunk for a while (presumably to clear some plague, though no reason is actually mentioned). It's fairly incidental.

The Nutmeg, being totally clean, doesn't have stinking bilges, and they acquire a preference for keeping their ships cleaner through running in water and pumping it out every day.

The're eventually rescued, by Chinese coming to the island to harvest birds nests (Maturin is incensed that the bird in question is not in fact a swallow at all, but merely a dimunitive Oriental swift).

And they get to Sydney harbor and Botany Bay, and see the total squalor of the penal colony, and the total corruption of most of the soldiers running it.

And they do find Padeen, who had been transported for robbing an apothecary to get the laudanum he had become addicted to (in fact, he was sentenced to hang, but Jack had enough influence to get in commuted to transportation). Jack is very upset that Steven is planning to take Padeen with them, and Steven is very upset that Jack won't go along with it. But I see no sign that he gets poisoned by the platypus as a deliberate ploy to cover Padeen's rescue; it seems like he really didn't know. The animal is not at all well-known in Europe, and there are few naturalists writing reports from Australia, and in fact it's known there primarily as a "water mole", which Steven doesn't realize is his platypus.