I see Spotify can work on the Apple Watch cellular without having the phone nearby. Is this an Apple problem or a google problem? Is there some way to request an standalone YouTube music app for Apple Watch or support from Apple?
Apple Watch SE
It's upto developers to develop apps for the Apple Watch, like the iPhone. YouTube need to make this, not Apple unfortunately.
Apple provides the hardware, API and operating system. Devlopers write the apps you seen the App Store for iOS, macOS, iPadOS and watchOS. Apple provide their apps (such as Apple Music) almost the same way other developers would, just tend to be more pre-installed as its Apple.
It is all up to Google. YouTube Music is their service, and they hold the encryption keys, so they need to provide an Apple Watch client.
You can tell Apple directly about your wishes for future watchOS features by using the Feedback link:
Why is there no standalone YouTube music app for Apple Watch
