Is ghusl obligatory after wadī if it causes the sensation typically associated with the emission of manī, as mentioned in a hadith of unknown authenticity attributed to one of the Companions?

The emission of al-wady does not necessitate ghusl (ritual bath) by consensus. Rather, ablution (wudu') is sufficient for it. This is what was reported from Mujahid in Kanz al-Ummal, where Ibn Abbas issued a legal opinion to a man, saying: "It is nothing but this chill, and ablution suffices you for it."