That's correct. It's a bit of a meme on twitter where someone will make some statement, then that phrase. Eg "20k seagulls die every day from choking on keurig pods. Let that sink in." Musk is parodying that with a physical sink.

yes. Let that "sink" in.

Yes, that's probably why. Musk likes dumb puns. Or maybe knows that his fans like them and that it gets attention without saying anything real.