I have a question: One of the conditions for the sacrificial animal (Uḍḥiya) is the flowing of blood. So what does that mean?

Shedding blood is a general condition for every sacrifice, as the Prophet, peace and blessings be upon him, said: "Whatever causes blood to flow and the name of Allah is mentioned over it, then eat." If the intention is that shedding blood is a condition for the validity of the sacrifice (udhiyah (definition)), such that nothing else can take its place, then this is correct; because the obligation is linked to the act of shedding blood, and the principle is that if an obligation is linked to a specific action, nothing else can take its place.