What kind of URL do I need for a custom song to play? I tried a YouTube link and a file link for TCRF where I first found it, neither of them result in any sound in-game.

Fan-made 2D Mario level designer · By
SMC can't use YT/TCRF links because of the way the sites are coded (or something similar to that.) If you want a custom song, you have to use Dropbox or File Garden. However, the URL format for those is different.
EXAMPLE: https://dl.dropboxusercontent.com/scl/fi/te2dz9er7kvaioyaie0eh/UFO-50-Maria-s-Theme-from-R...
All that's needed is for you to upload the audio file to dropbox, set privacy settings to "ANYONE WITH THE LINK" (or similar), set "www" to "dl", and add "usercontent" after the word "dropbox".
Figured it out. For anyone who reads this, use File Garden instead of Dropbox since it's easier. Just grab the .ogg file of whatever song you want (other formats may work but I used .ogg), go to your garden in File Garden, click upload, then copy the link to your clipboard and paste it into the game. Unfortunately, many songs (like the one I was using) have fadeouts at the end and you can't skip the last part like the first so you can't really get a good loop for those songs.