That's an interesting question and it's quite possible the medium matters about gravitational transmission speed. I.e. the question is how is gravity transmitted. We'd need to know a lot more about the structure of subatomic matter & interactions to answer this one. As it stands, we have no theory of gravity at all at the quantum level.

I'm firmly of the opinion there's no "spooky action at a distance". All waves propagate gradually (if rapidly) through a medium, even if we decide to call that medium "vacuum" and define it as empty. Or more modernly, a "field". Waves don't propagate in nothing by definition.