I wonder what the odds are that some deep sea salvage group is moving to collect that this very instant (or being contracted for such). If Starship lives up to even a fraction of its potential, that [not so] little guy is going to have some serious historicity.
They had a plane flying in the area shortly after landing, probably to drop some marker for a group to come around and recover the black box. I think they've stopped bothering with preserving the test articles though, in the process of test driven development, they're going to have so many "historic" test articles, that it's kind of pointless.
They still would've been in position to put down a marker, since they had to be prepared for that before they knew they'd be able to maintain telemetry down to the water, and if they're already in position, it doesn't hurt to place the marker anyway.
According to ChatGPT, a Starship has 1000 cubic meters internal volume, and weighs 120 tons empty, which my manual math says is a density of 0.12, which means it should easily float in the ocean.
It looked like the booster exploded when it submerged after soft splashdown. There was some fire and the stream cut off. Maybe that's what happened to the ship too.
I think they had a tug go out to drag it to deeper water and make sure it sunk - there was some ship (ocean) commentry I saw in a couple of places showing the tracking data.