I'm wondering if they had any tools or techniques that aren't as well known as conventional survival techniques (such as rubbing together of wood) or any that have been lost to time. Even any that you think might be interesting and unusual. Any thoughts?
The major difference from what we do today is that we think of "wilderness survival" taught to those who don't normally need it. For the Egyptians especially, this is how they managed everyday life. Making things in an osteo-ligno-lithic technology - bones, wood & stone - is how they got the ordinary jobs done. While they had bronze early (Old KIngdom), that stuff was expensive, so that stone knives remained more common than bronze. The ordinary archer in their armies shot arrows of reed with stone tips.
Through all these cultures, fire-making was avoided when possible, because it's a time-consuming nuisance. They smoored their fires overnight and carried coals in firepots when they could if they were travelling where they expected to have no one around from whom to borrow fire.
Sparks for fire starting could be provided by striking two flints together, even before the Iron Age provided steel and flint strikers. BTW, that's pretty much firestarting until the arrival of the self-striking match methods in the 1800s. A shower of sparks on good tinder will get you an ember to nurse faster than most all-wood techniques.
Interesting and unusual can be how to find, not the points of the compass, but rotational points with sticks and string. This may have been used to site temples and tombs.
Before noon, drive a stick into the ground, and drive a second one at the tip of the first one's shadow. Draw an arc centered on the first stick with the second on its perimeter. Wait until afternoon when the shadow touches the arc on the other side. Draw a straight line through that to get east and west. Construct a line at right angles to get north and south - rotational, not magnetic.
That one comes from How to Stay Alive in the Woods, but it helps explain why so many ancient sites do not match magnetic north & south.
Frankly, I think we have much better survival techniques, because we borrow out of everyone's traditions, use science for things like simple solar stills, and simply pay attention (well, some of us) to survival skills.
Ancients mainly had the advantage of knowing everything edible in their vicinity, because they needed it in times of famine. Earlier ones had OLL skills. Turning rocks into tools is invaluable. But the average Legionnaire was doomed if the supply trains couldn't reach him and he was off his home turf with no one to take food from.