I've been playing this game for many hours lately (it's the best version of Civilization that I've ever played!), through several full games. I have never seen a "depleted land" improvement on a tile. I only just learned from the Civilopedia that depleted land might even be in the game! Is it still in? I know I've used lots of slash-and-burn farms, so I should have seen it by now if it existed.

If it's been removed, that's too bad. I don't like the idea that slashing and burning should be eternally sustainable!

No, it doesn't. The slash and burn improvement has been repurposed. Also, at the time in game when it occurs, the scales were such that it was "kinda" eternally sustainable, as there weren't that many people around yet for it to have a really major impact. Probably.