How do I make this RANDOM model inserter only find models from the Library?

The solution is to check if the model:IsA("Model") and if it's the case, add it in workspace.

I went ahead and organized your script. What it does is generate a new model every 3 seconds. It checks if the model exists and if it does parents it in workspace. Then it runs a coroutine to destroy the model after a random amount of time while it can continue generating new models every 3 seconds.

Here's what it looks like:

local InsertService = game:GetService("InsertService")

local function ModelExists(modelID)
	local model
	local success, fail = pcall(function()
		local model = InsertService:LoadAsset(modelID)
	end)
	if success then
		print("Is an existing model")
		return true
	end
end

local function DestroyItem(whichItem)
	wait(math.random(1,100))
	whichItem:Destroy()
end

local function GenerateModel()
	print("Generating new model")
	local min = 1
	local max = 9999999999
	local modelID = math.floor(math.random() * (max - min) + min)
	if ModelExists(modelID) then
		local model = InsertService:LoadAsset(modelID)
		-- If you want other things as well then simply add 'or model:IsA("Part")' 'or model:IsA("UnionOperation")'
		if model:IsA("Model") then
			model.Parent = workspace
			coroutine.wrap(DestroyItem)(model)
		else
			GenerateModel()
		end
	end
end

while wait(3) do
	GenerateModel()
end

Let me know if that answers your question!