Re: "Apple Watch Music no longer has search option: I always used to stream music through my watch using the Search button without my phone and don’t use any saved or downloaded music, ever"
Apple support's online article for Watch OS 11: Play music on Apple Watch - Apple Support
Eg: says:
After you connect Apple Watch to Bluetooth headphones or speakers, then
Go to the Music app 
on your Apple Watch
Search the Apple Music library:
Tap Search, enter an album, artist, or song, then tap Search. Tap a result to play it.
Seems you really should be able to search ok while wearing bluetooth headphones etc.
So you may want to try restarting your Watch: ie:often restores order if something isn't working as expected
See How to: Restart Apple Watch - Apple Support.
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Re: Also, when I click on radio, I can’t select any stations.
See if Apple Support's guidance on how to: Listen to radio on Apple Watch - Apple Support can help:
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Useful Resource for Watch OS 11: Apple Watch User Guide - Apple Support
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If you need more help or support: (eg: online chat / phone / email ec.)
There is a "Get Support" link (scroll to the very bottom) on each of the websites (links below)
Music Support Website: Music - Official Apple Support
Watch support website: Apple Watch - Official Apple Support
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If you'd like to send Feedback to those who work on Apple Music behind-the-scenes:
There's a web-form available for that: Feedback - Apple Music - Apple
