Basically, this mod would be a Settlement item (eg: Resources > Miscellaneous > Auto-Equip Settler Container) that is a large, existing container; you place the container in your Settlement. Once dropped, you exit Build mode and dump all the weapons, armor and clothing you don't want into it. Then after you've finished loading it up, you "Activate" it and it equips all the Settlers inside your settlement with the equipment.
I've collected a ton of weapons, clothing and armor; but I cannot be bothered walking around to all my settlements adding these items to each the NPC settler. There's over 20 of them!
A later staged version of the mod could perhaps copy the way Local Leader > Supply Lines works and link multiple Auto-Equip Containers at each settlement.
In terms of lore or RPing, this makes sense because the settlers are meant to be people. They should be able to equip themselves.
NB: Could also be called SETTLEMENT ARMORY, but people would probably expect an actual armory building that could be built then (later version?).