A pendulum in zero-g is more like an orbit, a free hand of a clock, a
Ferris wheel. SHM no longer applies.
So if g vanishes instantly the Ferris wheel has rotational speed equal
to the lateral speed V of the pendulum at that instant. The new period
is simply C/V where C is the circumference of the circle (2 pi L).
There is no difference in behavior depending on the observer.
A related interesting case is if the cable is cut, not at the instant
the pendulum reaches mid-swing, but at end of swing. In that case the
string, the bob, and the elevator all drop as if freeze-frame.