Whenever "consume_item" in
"cost": {
"item_id": "arrow",
"consume_item": false,
"cooldown_duration": 10
}
}

is set to "true", a fourth arrow will be used, resulting in 3 shots that cost 4 arrows

How to recreate:
Make a new instance and install archers
Make a datapack to set "consume_item" to true
Enter a world, enchant an archers manual, and use "Barrage"
See that four arrows were taken from your inventory, but only three are on the floor that can be retrieved

archers datapack.zip
This is my datapack if you need a quick example, but it also will remove "Roots" and "Magic Arrow" from the ability list, so don't worry about that if it ends up confusing you

Upon reivewing the details I can tell you everything works as expected.
If you don't want the spell cost item to be actually deducted upon casting, than don't use such datapack. :)