I'm experiencing the same problem. In contrast to what Dorain1 says, I believe it has nothing to do with the availability of Apple Music in your location, as Apple Music is actually supported in Azerbaijan according to Availability of Apple Media Services - Apple Support, and, obviously, if it was not, it would've been impossible for you to experience this particular problem (you wouldn't have had an Apple Music service to link...).
Anecdotal evidence suggests that linking Google Home to your Apple Music service is currently supported in only several countries. According to https://9to5google.com/2021/12/09/apple-music-google-home/, these countries are: (1) Australia, (2) Canada, (3) India, (4) Mexico, (5) South Korea, (6) USA, (7) UK, (8) France, (9) Germany, and (10) Japan. According to the more recent https://www.reddit.com/r/AppleMusic/comments/vjzs1e/apple_music_for_google_nest_speakers_available_in/, a few additional countries are supported.
It's unclear whether this limitation is set by Apple or Google.