> If I want to go jogging without my phone, is it enought having with me my watch and airpods to be able to listen to spotify or apple music?
I can't speak for Spotify, but you can play Apple Music via your watch without your phone. You have two options.
If you have your watch connected with a cellular account, then you can play your entire Apple Music catalog via the watch, streamed via the cellular connection.
If you don't have a cell-connected watch, you can side-load music from your phone (identify specific tracks/playlists to copy to the watch). You're limited to how many tracks you can transfer to the watch (if you have a large library, it may not fit entirely).
Add music to Apple Watch - Apple Support