Hello rahulm97,
Thank you for using Apple Support Communities. It's our understanding that the YouTube Music app isn't working as expected on your Apple Watch. You've done a great job trying to get this resolved. We're happy to help.
Make sure that your Apple Watch and paired iPhone have the latest software.
Update your iPhone, iPad, or iPod touch
Update your Apple Watch
If the issue persists, restart both devices. Restarting can resolve many unexpected behaviors.
Restart your iPhone
Restart your Apple Watch
Let us know the results. Be sure to include additional error messages and any other troubleshooting steps that you may have tried.
Have a great day!