Functional Storage's quest "My First Drawer" in the Basic Storage chapter allows you to craft any storage drawer of any wood type by use of the #storagedrawers:drawers tag that is on every drawer.

Sophisticated Storage has a #sophisticatedstorage:base_tier_wooden_storage on the base tier of both chests and barrels, but is missing tags on the higher tiers. Adding these missing tags can allow the quest line for Sophisticated Storage to be changed to accept either barrels or chests of any wood type. The quest names will also need to be changed to something like "Iron Storage", "Gold Storage", etc.

Below is the KubeJS script I use to add the tags:

ServerEvents.tags('item', event=>{
	// Add missing tags to sophisticated storage
	['iron', 'gold', 'diamond', 'netherite'].forEach(tier => {
		['chest','barrel'].forEach(type =>{
			event.add(`sophisticatedstorage:${tier}_tier_wooden_storage`, `sophisticatedstorage:${tier}_${type}`)
		})
	})
})