It is not possible to register a device on your Microsoft account using a serial number, that process only works for Microsoft manufactured devices like a Surface laptop.
For all other devices, ensure you log into Windows with your Microsoft account, then in the settings app, go to the location settings and ensure you have Location services enabled for all apps and also the 'Find my Device' setting, then that device will be automatically added to your account online, it will not happen immediately, but it will happen.