To add to comments already made on this thread, the concept of a navalised Typhoon relies on a thrust vectored variant of the EJ200 engine to allow for a much reduced approach speed.
Already ‘bench tested’ thrust vectored EJ200s can apparently be fully integrated into Typhoon’s advanced FCS, allowing pilots to fly the steep approach path while the FCS manages engine nozzle position.
Take off would require a ski jump deck rather than catapult. Detailed piloted simulations, some of which were shown at Aero India recently, show the aircraft can take off in this way with a full weapon and fuel load!