Not seeing my Music library from Mac on my iPhone/iPad

Folks,

Do you know how I can SEE my WHOLE music library on iPhone and iPad with new Music App in Catalina?

My master library is on Mac, but I still don't see any new additions from CDs to it on my mobile devices.

I see pretty old playlists and new purchases from iTunes, but NOT the downloaded CD albums.

I don't want to sync them/download them to other devices (storage issue), I just want to see them in cloud on iPhone/iPad to be able to play them if needed.

I am using iTunes Match. "Sync Library" is on in Settings -> Music. "Show Apple Music" is on too, just in case. Signed out and in on all devices, to no effect.

Does it mean, that I can only see Apple purchases showing on all devices and NOT other downloads? Or is there a fix?