player should be of type Player, but is of type nil?

The full Error:

MarketplaceService:PromptProductPurchase() player should be of type Player, but is of type nil

The code:

local Players_ = game:GetService("Players")
Players_.PlayerAdded:Connect(function(plr)
	TheLocalPlayer = plr
end)
local Market = game:GetService("MarketplaceService")
script.Parent.Activated:Connect(function()
	Market:PromptProductPurchase(TheLocalPlayer, 1130818996)
end)

This is a LocalScript and it's in: StarterGui>ScreenGui>Frame>TextButton>LocalScript

Note: I probably know how to do a workaround for this, but I do want to know exactly why this happens so I can educate myself on that. Thanks! :D

the error means the typeof(player) is nil and not a player instance, so fix as shown and it should work:

local Players = game:GetService("Players")
local TheLocalPlayer = nil
Players.PlayerAdded:Connect(function(plr)
    TheLocalPlayer = plr
end)
local Market = game:GetService("MarketplaceService")
script.Parent.Activated:Connect(function() -- not sure what you want activated for a prompt to show up but here we are
	if TheLocalPlayer ~= nil then
   	 Market:PromptProductPurchase(TheLocalPlayer, 1130818996)
	else print("localplayer was nil") end
end)

didnt test this and never used prompt purchase so it may work on the client but i think you get my premise

When you declare a variable without using local, Roblox makes it local for you. This is both a benefit and a pain to deal with if you plan on actually declaring global variables (but _G exists for this reason).

In terms of how to resolve your issue, you are going to need to declare a blank variable on the base scope (the variable doesn't have to be assigned to anything to be declared) and then assign its value when the time comes.