What's amusing is you could always tell the keyboard players back then, by the way they slowly turned around.
Anyway, playing with the mouse was a new thing. Mouse acceleration, dpi, etc. were all just experiments. Introducing a new way to move would surely uncover bugs hidden in the physics code that simply weren't possible to hit with keyboard movement.
IMO back then you discovered it either by just playing, or by reading a game magazine. Back then (when Quake II was released), internet guides for games were less streamlined and available. Which was fun for gaming, as you could discover things on your own. It also meant things had to be less min-maxed. Think of a game like World of Warcraft or Diablo when it was just released, they have the very same problem.
We knew, that there is maximum forward and sidespeed but they way they add together is simple vector addition, so you could actually get higher maximum forward speed if you could point that vector forward.
We knew it is possible to preserve momentum when turning in air. We abused this jumping outside of ledges and then turning and going back to where you came from. This was very useful on dm2 where there is a ledge, a pool of laval and a wall that divides the ledge. You are supposed to press a button to actuate a ramp on which you could cross the lava but you could also just jump and turn in air violating any physical intuition. The jump can be seen here https://youtu.be/VT-johLi75w?t=128. This jump has a bunny hop component to it but it is not necessary.
Hopping wasn't discovered immediately. I remember we were doing things like strafing into walls to speed up movement before we knew bunny hops are possible.
I don't think idSoftware predicted how the game would be used when they were working on it. I believe the movement mechanics is just a byproduct of simplistic movement calculations.