Does a setup with TRS and transmission need a neurtal saftey switch in order to swith gears?

No it should not. The neutral switch keeps the boat from being started in gear.

Alpha and Bravo boats have a neutral switch and a shift interupter that momentarily cut out the ignition when shifting

Only Alphas have the interrupt. Both have neutral safety switch, the later TRS probably do as well. Bravos and TRS have no interrupt.