Sync playlists on iPhone and iPad without a computer?

I no longer own a computer. I have no need for one personally, since all I need to do outside the office is read, write, and listen to music. When I recently purchased an iPad Pro and set it up with my Apple account, the music on my iPhone (that had been backed up on iCloud) appeared on the iPad. This included the playlists I’d set up.

I’ve just made a new playlist on the iPad, but it hasn’t shown up on my phone. It’s been a couple of days now, so plenty of time with both devices being connected to the cloud. Can anyone explain the ins and outs, and why the playlist hasn’t appeared in both places?

Many thanks.