Tires will have some impact, but I would not expect it to be as large as you might well be imagining. Keep in mind that rolling resistance tests are done under an ideal lab conditions whereas the roads that many of us ride on are far from that (even if not always fully gravel). The GP5000 may still be faster on a moderate road condition, but the difference is likely reduced when presented with the real world.
Perhaps more importantly, rolling resistance is only a small component of the forces acting against you. At 30kph, 90% of the resistive force is from the wind. (I'd link to the site making this claim, but not allowed as a new member - you might search for something like "fascinating-aerodynamics-bikepacking-bicycle-touring" to find it. Bicycle Quarterly also has an interesting article on the subject.)
I note that your riding position looks rather upright - both the stem position (although difficult to see clearly in your picture) as well as the brake hoods. Clothing is another factor - loose fitting clothing is a much larger factor than rolling resistance, as is what sorts of stuff you attach to your bike (and where).
I'd look over your clothing selection, and see if you can adapt to a more aerodynamic position before necessarily spending a bunch of money on tires (and maybe wheels) that might not make all that much of a difference.