How can I view my entire iCloud library?

I have had iTunes Match in the past, where I had downloaded songs and added them to my iCloud library, with some matching. I then cancelled my subscription to iTunes Match, and deleted all those songs (I wanted to start my collection from scratch). Since then, I have subscribed to Apple Music.

Weirdly enough, when I connected my last iPhone (which then was destroyed by water damage so cannot be used anymore) to my Mac, and had Apple Music turned off, I saw an entire library of songs on my phone (which are NOT in my iTunes library) that were from when I had iTunes Match.

I would really like to retrieve these songs, or at least see a list of them so I could know which songs to download. Why did they appear on my old iPhone when I connected it, but are nowhere to be found on my Mac or new iPhone?

Many thanks.