The rolling resistance website linked is a helpful start, but leaves much to still guess.
I don't run a 32mm road tire at 44psi or 33psi, which are the listed free options. I would guess that at 65-70psi, the 32mm gp5k would be at 12w of rolling resistance.
Then you can see the 42mm Specialized tire was tested and you have the 38. So if that 38 were run at 50psi, then it would probably be 20w of rolling resistance.
Compare 12w to 20w, that's a best guess using the actual widths you want and general tire pressures that would likely be used for road riding in the given widths.
You will drop something like 370g of combined tire weight by going from the 38mm Specialized to the 32mm GP5k tires and that is nothing to ignore as it's over 3/4 of a pound.
As mentioned though, your riding position is going to be a huge difference maker on speed as you are a way bigger drain on speed than the difference between those two tires.
Figure out how to ride long stretches with your elbows bent and tucked with your hands on the hoods.