I was looking at the legendary weapon effects wikia page and came to the two shot entry. It says that it "fires an additional projectile." I remembered that I recently found a two shot combat shotgun. Does its prefix mean that it fires one more pellet or twice the pellets when compared to a normal combat shotgun?
Well, let's put the speculations aside and test it experimentally!
If we compare two identical stock double-barrel shotgun (With a long barrel) in our inventory, we can see that the predicted damage for the shotgun with Two-Shot is already twice the damage of the standard shotgun:
If we test it point-blank on a gentle Deathclaw, we can observe the real damage difference between the two shots, which is just over 2x:
The slight difference can be explained by the pellets spread. I tried to reduce it to the maximum by using the Long Barrel mod and having my character placed at the exact same spot, doing a Body shot in VATS
So, in conclusion,
Per your link to the Wikia:
This means that 2 rounds will be expended. Here are some examples that will help answer your question: