Hi, gsvarghese!
Thanks for reaching out to Microsoft Community and posting your concern regarding your Bluetooth headset on your Surface Pro 7.
May we know if you still see the headset inside Control Panel?
Please go to Control Panel > Hardware and Sound > Devices and Printers.
If you do, please remove it and try to add your headset again.
If you still cannot pair it, try pairing your headset to another host device.
If possible, try another Bluetooth accessory and connect it to your Surface Pro 7.
Also, please run the Bluetooth troubleshooter.
Go to Settings> Update & Security> Troubleshoot.
Look for Bluetooth, then run its troubleshooter and follow the instructions.Try adding back your headset.
Run Surface Diagnostic Toolkit and make sure to complete the tasks.
Let us know how it goes.
Kind regards,
Janette_Z