2001 Chevrolet Silverado 1500 - Heating issue

heater blowing cold air ,climate control working ,actuator door working,water going into core hot coming out cold

Coolant constantly flows through your heater core, whether you want heat or not

So you’re talking about the blend door actuator . . . ?

So you’re saying one heater hose is hot, while the other is cold . . . ?

Assuming the engine had reached proper operating temperature when you made that statement . . . your heater core is at least partially plugged, maybe completely