Hi JustGC007,
As I understand, one can start working for the new company after application for transfer/new H1B. On its approval, the old H1B is no longer valid.
If one opts to work for a new company using EAD, the person is out of H1B status.
BTW, there should be a way to find out your current (H1B) status.
Good luck.
DIGS
EB3, India