Good day, thanks for your question. If you are able to connect the controller using a cable, it might be within the pairing mode where you are encountering an issue as well and you may refer to the below.
Controller is not in pairing mode
> Press and hold the small sync button on the top of the controller (this is next to the USB-C port) until the lights start flashing.
> You may now also go to Windows Bluetooth settings and pair it.
> If the sync button is not pressed, it will not show up for connectivity.
Controller might be connected on another device
> If the controller is already paired to a Switch console or another device, it will not be recognized that it can be paired pair to PC.
> If you are able to it connect via Bluetooth, then Windows might list the controller as a Pro Controller or it might also be listed as Input Device which will you will still be able to pair it from there.
You may also refer to the links below for additional guide.
https://www.pcgamer.com/how-to-use-a-nintendo-s...
https://www.wikihow.com/Connect-Switch-Pro-Cont...
https://www.lifewire.com/connect-nintendo-switc...
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Regards,
Paul R.