I am a bit lazy tonifht to go back in IMU wb but still curious ahah , could you quickly explain me why a torque would be choose over a matrix alignement and vice versa ?

I'm not 100% certain, but I think it's because of the Euler singularity - which is usually at 90 deg pitch up and down and confined to a point. Regardless of the 'true' gimbal orientation, you can always define a transformation that gives you a different system - except at the singularity.

But if you do so, the singularity expands from a point into a ring.

There's a practical example of this - Vitos has done the trick for Vostok, it utilizes the FG attitude computation but changes it into a system 90 degrees shifted - as a result the singularity encompasses the whole pitch=0 ring around the horizon.

What I'm guessing is that gimbals are torqued to avoid that from occurring by keeping the correction matrix shift as small as possible.

Does the SpaceShuttle have GPS, or is that a too "modern" invention for its avionics?

It sure does, but GPS doesn't provide attitude information. And Atlantis is a single string GPS vehicle - you can access GPS information, but there's no redundancy in case of a failure and so operationally you may not rely on GPS except in the case of a massive systems failure elsewhere or for testing and evaluation purposes.

(If you like, you can force GPS data into the state vector, and that's going to provide near-perfect position information).