What happens to my music library on icloud if I cancel Apple Music?

You can certainly store music in iCloud Drive, but that will not allow you to stream the music to your device.

You do not need an iCloud Music Library to sync music to your device using iTunes or re-download purchased iTunes tracks.

The word "cloud" has a few contexts around music. Your purchased iTunes tracks are stored in "iTunes in the Cloud" You can, as I say, keep music tracks in iCloud Drive and you can pay to have an iCloud Music Library.

Those are 3 different things. I am not sure how you are using the word cloud as relates to music.

iCloud does not have a music library feature outside of the paid options I have described.

I don't know what this means if it's not a paid iCloud Music Library.

>>> My own library exists only on iCloud, bc I've got rid of my old CD's

An iCloud Music Library is a benefit of a paid subscription to either Apple Music or iTunes Match.

Once either paid subscription ends, you no longer have access to your iCloud Music Library.

Can I use the music-app on my iPhone to listen to my personal library as I did before I subscribed to Apple Music?

Yes, Your CD based music is still available on your computer, but it is not accessible over the air.

My own library exists only on iCloud, bc I've got rid of my old CD's to save space, and my old Mac with the backup files are not cooperative anymore.

The iCloud Music Library is not considered to be a backup of your personal music.