What is the world record for fastest speed unpaced, upright, on a road bike, on the flat, outside, in regular clothes?

Until there is an "International Union of Regular Guy Cyclists," there will be no measured record for this because cyclists who are contending for records use the best equipment they can, under the best conditions they can find.

Aerodynamics are very important in cycling, and the faster you go, the more important they get. Elite sprinters reach ~45 mph in 200-m sprints, which takes ~1700 W (depending on weight). 40 mph would require ~1200 W. But this is assuming form-fitting clothing in a tuck.

There are two factors determining aerodynamic drag: frontal area (the size of the hole you are punching in the wind) and drag coefficient (how slippery you are relative to a flat surface). These are usually multiplied together to produce a number represented as CdA.

Your bike position affects both terms: the Cd part and the A part. You might have a frontal area of .533 m^2 on the tops, .426 m^2 on the drops (1); your drag coefficient on the tops is 1.15 (literally worse than a flat board), on the drops 0.70 (2).

You can plug these numbers into this calculator to get some ideas of the wattage you would need under different scenarios. If you want to ride at 40 mph on the tops (and you have a normal weight for a fit man of average height), you need to produce 2250 W, which is superhuman. Note that this doesn't take into account clothing aerodynamics.

Specialized has their own wind tunnel, and has produced a bunch of videos showing how much you can benefit from various changes to your setup. Here's one for clothing, and one for position. They don't express their results in terms relevant to sprinting, but they're still informative.