Hello LucasDinh,
Thank you for reaching out to Apple Support Communities, and we'll be happy to help in any way we can. We understand you're having issues with playing Apple Music on your watch and your iPhone with AirPods. To clarify, are you trying to play music on both simultaneously? If so, that isn't something that is available to do. You can find information about playing music on your Apple Watch here: Listen to music, podcasts, and audiobooks on your Apple Watch
"If you're connected to Wi-Fi or cellular on your Apple Watch Series 3 or later, you can stream Apple Music, Apple Podcasts, and audiobooks, even when you’re away from your iPhone.
You can also sync music, podcasts, or audiobooks from your iPhone to your watch. Then you can play the content on your watch without your iPhone nearby, even if your watch is not connected to Wi-Fi or cellular."
If you're trying to sync music to your watch, check out the section of that article titled "How to sync music to your Apple Watch"
We hope this helps.
Cheers!