Why do gas water heaters require external venting while gas stoves do
not? Is there something fundamentally different in the combustions
byproducts (CO vs. CO2) that need to be vented for the water heater
and not the stove?

If the only reason is the volume (BTU rating) of byproducts, it
doesn't make sense. For example, a moderate water heater can have a
rating of 75,000 BTU, while a high end stove will have a total BTU
rating over 100,000.

Worse case, think about cooking a Thanksgiving meal, oven is on for
six hours and all the burners are going, all this is vented inside the
house. While downstairs the water heater just has a pilot light
going. Why is one required to have external venting while the other
one doesn't?