If someone doubted that they had committed one of the nullifiers of Islam, then pronounced the Two Testimonies (Shahadatayn) and performed ghusl with the intention of removing major ritual impurity (janabah) and entering Islam, but then their wudu was broken during the ghusl by passing wind, should they complete their ghusl and then perform wudu, or must they repeat the ghusl with the intention of (entering) Islam?

You are afflicted with waswas (obsessive whispering), and we warn you against succumbing to it. If you doubt the invalidation of your Islam, the default is that you are a Muslim until you are absolutely certain that you have committed an act that necessitates disbelief (kufr). Ghusl (ritual bath) is not obligatory for a disbeliever unless he commits an act that necessitates ghusl while in a state of disbelief, in which case he performs ghusl to remove his ritual impurity, not because disbelief itself necessitates ghusl. And according to the view that ghusl is obligatory upon embracing Islam absolutely, the emission of wind does not invalidate it. You were not originally required to perform ghusl due to your aforementioned doubt.