You have no idea how huge the sun is.
By mass, the sun is much larger than the rest of the solar system with the earth and all other planets.
The sun is 1,300,000 (1,300,000) times larger than the earth. Even if the whole earth is turned into a huge, blazing nuclear ball, nothing will change.
The concept of nuclear deterrence will disappear and there will be another world war.
(as an option)
What happens if many, many, many, many matches are thrown into a blazing house? Nothing will happen. They will burn.
Humanity has not yet matured to the level where it could somehow influence the Sun. And this is good news.