Most wars are fought over property (land, resources, etc.)

A society that isn't based on property would have a lot less to fight about.

And most anarcho-comnunist style social structures are thought of as being post revolution. So it will be war to get there, but an economic war fought by workers against the oligarchs using solidarity and work stoppages as the weapons.

Solidarity, taken as a value, is another way to prevent war between the syndicates. Everyone would be workers and fighting against other workers would be socially unacceptable. Like dropping a fart in a crowded subway car, no one wants to be the one doing it.

I do expect there would still be conflict. Two syndicates may both want a rare resource. I imagine each syndicate would be able to elect a representative to some sort of larger democratic body. Like the UN, but without all the fucked up veto powers by nuclear armed states that prevents our actual UN from having any real power.

edit: Buddhism has existed for 2500 years as a loose connection of syndicates without serious infighting. Letting go of property and focusing on community goes a long long way.