Because the Bronze Age in Europe spanned (approx.) the years 3000-600 BC.
I suppose that the battlers of the time would make use of whatever weaponry and equipment that was available to them including a mix of older (wooden) and newer (bronze) weapons.
The victors and anyone else who came upon the site would likely have scavenged anything of value from the dead and leave the old or broken weapons behind at the scene.
“The weapons used were apparently arrows and wooden clubs, so how is it they call this a “Bronze Age” battle site?”
Simple. The winners simply picked up all the bronze spears. Bronze was valuble.
The spears were probably made in Brittany. Wouldn’t you pick up a Brittany Spears?