If I was having this problem, I would be doing a fuel volume test.
I have had pumps with a weak lever return spring, that would just not pump sufficient fuel at idle.
If the volume is not there, do not condemn the pump yet; it may be a restricted delivery line.
If you see bubbles in the delivery, it could point to sucking air, or it could point to something in or near the entrance to the pump that is dissociating the fuel.
