OK, so while a lot of different technologies are going to go out of favor because they require unsustainable resourcce use, there are a few things humanity as a whole has come up with that might be adaptable. Personally, I think steam power may be one of those things.
We’ll still be able to boil water. Holding any kind of pressure would be another thing, but it might be do-able with ceramics. (another post on that after some research.) It will require some tinkering, but I think the primitive steam engine is a possibility. What it could be useful for, other than a curiousity, is questionable, I suppose.
But basically as long as metalworking is possible, steam power is possible. More interesting still is stirling engines. These engines merely run off a temperature difference between two points on the device, and a simple one can be made from a tin can, a balloon and balsa wood. it also works in reverse, like an elecctric generator. You turn the axle, and one side gets hot while the other side gets cold. They are more frequently used in their capacity as heat pumps.
What am I getting at? Basically that mechanical advantage could be around a long time. The immediate, non-harmfull uses I can think of are turning grinding stones or powering a small generator. Also, a stirling-type heat pump could be hooked up to a windmill to heat or cool a home, or make a modern-type kitchen (cool side for refrigeration, hot side to cook on.)