Hello Ram Iyengar,
Welcome to Microsoft Community.
After reading everything you've posted, allow me to first recommend to you the scheme shared by another moderator, as it seems to be having the same problem as you when using Bluetooth headsets:
Why won't my surface pro 9 recognize my Bluetooth headphones? - Microsoft Community
According to this moderator, try switching from mono to dual in your sound Settings.
If that doesn't work, try referring to my reply, downloading the driver and firmware package for the Surface Pro 9 and installing it.
Best Regards,
Mitchell | Microsoft Community Support Specialist