For running, I was used to using Google Play Music to hear music offline from my phone.
Now Play Music will soon be closed and YouTube Music does not offer offline listening for free.
So I had to look for a way to synchronize my Google Music Playlist to another service like Spotify.
(With Spotify Premium you can download a playlist to your phone and here music offline, without internet connection - even if this account is used by someone else e.g. in your family)
I share here the solution I have found.