Hi Mackgraham,
welcome to the Apple (user-to-user) Community.
Re: album: "add music doesn’t give options to add to playlist".
Am no expert in this area, yet your question surely deserves a reply.
Seems playlists are mostly for individual songs rather than albums. I could be wrong.
It may depend on whether the album is on your device or in Apple Music online.
You may just need to add the songs from the album one by one, or maybe you create a special "smart" playlist just for that whole album.
Apple Support has articles online (links below) that have step-by-step guidance
How to make a playlist in the Apple Music app - Apple Support
Eg: says:
"You can also touch and hold a song, album, or playlist. Then tap Add to a Playlist to add the music to an existing one, or tap New Playlist. Or you can touch and hold on a playlist to download, share, or delete it".
or
How to: Create and manage playlists in Apple Music on the web – Apple Support
Eg: says:
"If you have the Music or iTunes app on your computer or device, you can do much more with playlists, such as create a Smart Playlist that updates automatically based on criteria you choose, or a Genius Playlist that includes music in your library that’s similar to the selected song. To open the app directly from Apple Music online, just click the link in the bottom-left corner."
All the best :-)