It seems that after Big Sur, Apple dropped support for MP3 CDs… which is very odd because they're just Yellow Book data CDs with mp3 files. I admit I don't know nearly enough about CD encoding to understand what's going on here, but the practical upshot is that no Mac running a recent version of MacOS will read an MP3 CD. I banged into this when I bought a CD audiobook recently.
There are exactly no useful answers on the various Apple forums, just people saying that you 'should' be able to just copy the files off the CD, which, er, just doesn't work.
I've found a workaround though.
Install the free trial version of Parallels Desktop. Let it download and install Windows 11. This will take bloody ages. Go and make dinner, or take the dog for a walk.
Once you have Windows up and running, plug your CD/DVD drive into your Mac and insert the MP3 CD. It'll appear on the Windows desktop in the sidebar and you can then either play the files with Windows or copy them across to the Mac side of things.
This worked for me with a 2020 Intel Macbook Air running MacOS Sonoma 14.3 and a Buffalo DVD±RW drive that's so old it has a mini-USB socket.