To answer my own question, and if anyone is looking in the future.

1. It is possible to walk from T3 to T2 airside. Once you are up the stairs from arrivals to departures, turn left and follow the signs to T2. You will pass by entry immigration, walk through a long corridor and a covered overpass, and arrive in T2 at security (which is centralized).

2. You can walk through T2 security, as they do not check boarding passes.

3. You can also get back to T3, althoigh there is no official route, so this involves showing your boarding pass to someone at security and being let through backwards through metal detectors.

4. However, if the reason you want to do so is to visit the (good) priority pass lounge, you might be disappointed. Lounge attendants were adamant that I can only use the lounges in the terminal of my departure flight and did not let me in. That's Egypt for ya.