What circuit capacity will I need for a strand of outdoor lights?
The limit of 33 bulbs in a string is based on each socket being limited to 40W (it will say that somewhere). 33 x 40 = 1320W, divided by the worst case scenario of 110V (nominal is now 120V, but many places still only provide 110V, so they have to cover that). So 1320W / 110V = 12A, which is the limit of what you can put on a 15A circuit breaker (80% load).

I agree that 350ft is a long distance for a load of 12A, but MOST people in the US will have closer to 120V, so if it drops to 110V, that's still covered. The problem may be if you only have 110V at the outlet, the voltage will drop even more. But on incandescent bulbs that just results in less light, not more current.

If you use LED bulbs however, where the equivalent light of 40W incandescent bulbs will only use 4.5W each, the current will go down significantly (less than 2A total) and there will likely be no perceivable voltage drop.