Heya! This could indeed be interesting, however there’s a lot of possible legal investigation to look into when it comes to music copyrights.
In the short term it’s hard to say how we could approach this. Long term we of course would love to expand our data and game info with music, sounds like an obvious fit!
Additionally, I don't know if this is helpful or not, but this is how Plex handles theme music for TV shows.
Awesome that you're considering it!
I've been trying to think of a way to create a music database myself and similarly trying to figure out the best way to avoid any legal issues.
One idea could be to just embed a youtube video to the theme song and let youtube take care of all the copyright details. example (https://www.youtube.com/watch?v=sGmvpt5o5Ws)
Another idea is to only have music which is licensed under creative commons. That unfortunately means a lot of game music won't be available. example (https://www.youtube.com/watch?v=7NO0bsMp1uw) This video is licensed under youtube creative commons license AND the user posted download links in the description of the video.
If you do implement anything to handle theme music it would be great if there could be multiple entries for the music. As well as an order (many games the music is per level so the order would be the order that the levels appear in). Lastly a type of music (enum list). 0 could be "main/title screen" for example, 1 could be "level", 2 could be "credits", 3 could be "intro music", 4 could be "other/misc" just as examples.
And maybe a long shot, but could twitch/amazon leverage the licensing of amazon music? I've not looked into this too much but I did see "Super Mario Bros. Theme" by 8 Bit Era is available on there. This probably is not the EXACT original theme song, but it's very close.