If the intention is severed during ghusl al-janabah, and the ghusl is completed with the intention of cooling off, or the ghusl is interrupted, is it permissible to renew the intention and consider what was washed before the interruption valid, especially when afflicted with waswas (obsessive doubts)?

If you are afflicted by waswasah (obsessive whispering from Satan), proceed with your ghusl (definition) (ritual bath) and pay no attention to the devil's whisperings that you have broken your intention. Even if you actually did break it, simply wash the remaining limbs, and you are not required to repeat the entire ghusl, because continuity (muwalat) is not a condition for the validity of ghusl according to the majority of scholars.