How can one add specific music tracks to Photo slideshow?

Its will depend on your system version, which songs you can select for a slideshow.

There are several possible reasons, why you may mot be able to select a certain song:

• On none of the system versions you can use protected songs for a slideshow - songs with a digital right attached that will prevent copying or modifying the song.Such songs are shown in iTunes or Music in the File tab of the Info with the "Kind: printed AAC Audio File".
• Streamed music does not allow us to use the song in projects. On some recent system versions Apple allowed us to use downloads from Music as a sound track for the slideshow or a memory video, but then we could not export the finished the finished slideshow as a video with the sound track included.
• Purchased songs from the iTunes Store (unless tagged as protected audio file) can be used at all system versions as a sound track in a slideshow, if the duration is sufficient.
• Ripped songs from purchased CDs (unless tagged as protected audio file) used to be eligible for slideshows in Photos until macOS 10.15 Catalina. Since then I could not use them on any newer system versions.
• Our own audio files (Songs we have recorded with a microphone, for example, when we are singing along to while playing a piano or our guitar) used to be eligible for slideshows in Photos until macOS 10.15 Catalina. Since macOS 11 up to macOS 13 I could no longer use my own handmade music for slideshow sound tracks. I would have had to offer my songs at the iTunes Store and buy them from there to be able to use them in a slideshow. It is working again in macOS 14.1, however, finally. Now I can again use my own singing along to my guitar recorded and mixed with GarageBand as a sound track in Photos.
• Songs stored in iCloud need to be downloaded to the Mac before they can be used as as soundtrack in Photos.