how would i make a script only run once per player and a counter that saves through servers?

You can either make a table and store player's name and then when someone passes it checks for the name, or you can use values that will be named by the player touched the part and then store it under script and check if it finds it. Example 1:

script.Parent.Touched:Connect(function(part)
    if part.Parent:FindFirstChild("HumanoidRootPart") then     
        local player = game.Players:GetPlayerFromCharacter(part.Parent)
        local label = player.PlayerGui.EndingGui.Menu.Easyendings.updatable
        if player then
          if not script:FindFirstChild(player.Name) then
            label.Text = tonumber(label.Text) + 1
            newVal = Instance.new("StringValue")
            newVal.Name = player.Name
            newVal.Parent = script
           end        
           end

    end
end)

Example 2:

local tabl = {}
script.Parent.Touched:Connect(function(part)
    if part.Parent:FindFirstChild("HumanoidRootPart") then     
        local player = game.Players:GetPlayerFromCharacter(part.Parent)
        local label = player.PlayerGui.EndingGui.Menu.Easyendings.updatable
        if player then
          if not table.find(tabl, player.Name) then
            label.Text = tonumber(label.Text) + 1
            table.insert(tabl, player.Name)
           end        
           end
    end
end)

For saving use DataStore service.