Unconscious enemies are difficult terrain
Jeremy Crawford points this out here:
What about unconscious enemies? Would that be a difficult terrain, at least?
The space of another creature is always difficult terrain (PH, 190). Many DMs let people walk over the unconscious.
No official rule on corpses
Jeremy Crawford states his own ruling as a DM here:
Do corpses left over from dead creatures create difficult terrain for the purposes of movement in combat?
As DM, I treat corpses as difficult terrain.
The fact that he's responding in terms of how he rules it as a DM suggests that there is no official rule on whether corpses - which are no longer creatures, as you point out - are difficult terrain. One could logically rule that being dead doesn't keep them from making it a little more difficult to walk over/around them.
In practice, many DMs don't treat them as difficult terrain
In all the games I've been in as a player, and the few games I've DMed (in person), it has almost never been ruled that the creature's corpse creates difficult terrain. The only exception to this experience has been with particularly sizable creatures, such as the Fire Giant Dreadnought, a Huge creature from Volo's Guide to Monsters.
All in all, the fact that there's a gap in the rules means that the DM is free to make their own ruling. (To be fair, they could still rule otherwise even if there were an official rule, but in this case they can do so and still abide by the rules as written.)