The variable $Service doesn't exist on the remote machine.
Change this: Start-Service -Name $Service to this: Start-Service -Name $using:Service.
The effect is to parameterize the contents of the variable inside the script block using the local variable on the source machine.
You should note that the Get-Service -ComputerName does NOT work in PowerShell 7. You should check the status of the services in the script block of the Invoke-Command if you want forward compatibility. That would also decrease runtime in PS5 by not making (and tearing down) as many connections to each remote machine.