Why does my script give a "stack overflow" error?

In OnActivated, you use recursion, which either never ends or repeats a lot. Since Roblox disabled tail call optimizations, you should consider using a loop instead of using recursion.

In your case, it seems like you're using recursion simply to repeat code with no new arguments passed. In this case, you'd just need a loop in the function like

local function OnActivated ()
    while IsActivated do
        --code in OnActivated
    end
end

Note: If you want to take advantage of tail call optimizations in Lua, return the return value of the function, eg:

local function foo()
    return foo()
end

You accidently fit a if statement that defines a function that the if statements defines You are making a loop of that function since its inside it.

local RemoteEvent = script.Parent:WaitForChild("RemoteEvent")
local Mouse = game.Players.LocalPlayer:GetMouse()
local Tool = script.Parent

local IsActivated = false

local function OnActivated ()

    local Target = Mouse.Target

    if Target then

        local Durability = Target:FindFirstChild("Durability")

        if Durability then

            IsActivated = true
            while IsActivated == true and Target.Parent ~= nil and Durability.Value > 0 do
               wait(0.1)
                Durability.Value = Durability.Value - 1
            end
        end
    end
end
  if IsActivated == true and Target.Parent ~= nil and Durability.Value == 0 then
                RemoteEvent:FireServer(Target, Target.Value.Value)
                -- focus
                if IsActivated == true then
                    OnActivated()
                end
                -- focus
            end

local function OnDeactivated ()
    IsActivated = false
end
Tool.Activated:Connect(OnActivated)
Tool.Deactivated:Connect(OnDeactivated)

You also set IsActivated to nothing, you declared the variable, but with no value. Which is an error universally for all programming languages. (Except for HTML or CSS, they aint programming languages)