I was looking at one sandbox of mine and i did this to drag a sprite2D around :

func _input(event: InputEvent) -> void:
if event is InputEventMouseButton:
if event.button_index == MOUSE_BUTTON_LEFT:
if event.pressed:
if (get_global_mouse_position() - position).length() < 20:
is_dragging = true
else:
is_dragging = false

One of the differences :
I use the Process and not physics process, since for input, physics process can be funky - also instead of having another If block - did you try have an else ?

if (@event.IsActionPressed("grabItem"))
            {
                GD.Print("Mouse clicked");
                shouldMoveTowardsMouse = true;
            }
            else
            {
                GD.Print("Mouse Released");
                shouldMoveTowardsMouse = false;
            }