Bluetooth connectivity issues

I have a MacBook Pro (13-inch, mid-2012 version) running on OS X El Capitan with Bluetooth 4.0 compatibility, which could not find or pair with my Sony headphones (type MDR-XB70BT) with Bluetooth 5.0 compatibility. From what I read online, Bluetooth 5.0 should be able to find and pair with Bluetooth 4.0.

Since I bought the Mac (5 years ago), I have never used Bluetooth (kept it turned off). And since I recently got these headphones as a christmas gift, I figured I would use it on my Mac.

I tried numerous methods such as deleting com.apple.bluetooth.plist, restarting the Mac numerous times. It’s still not able to detect it.

Both Bluetooth devices are in working condition.

Seamlessly, I was able to find and pair my iPhone 8 (Bluetooth 5.0 compatibility) with my MacBook. And I was also able to find and pair my headphones with my iPhone. However, I cannot find nor pair my headphones with my MacBook.

Any help would be appreciated.