None of that changes that it was an Iranian warship.

Warships of nations involved in armed conflict are always valid targets for the adversary.

Otherwise it would also have been a bunch of war crimes for the Iranian ships destroyed at the pier by cruise missile or bombs.

India was not a party to the conflict so they can't vouch for the unarmedness of a warship on either side one way or another. But even if they could, unarmed warships are valid targets for the reason the other commenter pointed out (they can quickly become armed).

Nor does international law necessarily require a warship to personally pick up all survivors, and in fact gives warships a fair amount of leeway to consider their own security along with their own ability to execute a successful rescue and successfully berth the shipwrecked.

Modern submarines, while not exempt, tend to fall into that proviso more than other classes because they are not equipped to conduct surface rescue (unlike WWII-era submarines they don't even have a keel for surfaced stationkeeping), have no brig facilities, have no sickbay and very little other medical facilities.

Once it was clear that the Sri Lankan navy (the closest ships to the Dena's survivors) was responding, the responsibility of the U.S. to see to rescue had been accomplished.

Edit: Actual legal experts go into this more at https://www.justsecurity.org/133397/sinking-iran-frigate-den... but this is basically a slam dunk.

Whether it was a good idea is a whole different question, but warships sinking warships is what is supposed to happen in war.