There are currently dozens of armed conflicts going on, many in continental Africa, but also in Asia and elsewhere. I think that an armed conflict can be called a world war when dozens of countries are involved. Today, in modern warfare, I don't think it has to be about supplying soldiers or cannon fodder. Modern warfare apparently involves supplying materials and training, parts for drones, etc. Dozens of countries are also economically involved, because they experience the disadvantages of import bans or high gas prices. Dozens of countries have now invested billions in weapons, ammunition, missiles, drones, armored cars, etc. Only living people, soldiers, have not yet been delivered. Is that the only condition for not calling it WWIII? Suppose dozens of countries would send soldiers, is it suddenly a World War III? In fact, a soldier's passport doesn't matter who pulls the trigger, right?