I'm missing a ton of music that I had after factory reset

Music is not part of the backup.

You would have to re-sync it from your iTunes library.

Unfortunately, you don't seem to have an iTunes library any more.

You would have to obtain a Windows PC or Mac and re-rip your CDs or re-import the ripped MP3 files, then sync the music back to your phone.

Note that if you no longer own the CDs the music was ripped from to begin with, you no longer own the music at all.

You may be better off at this point looking at the Apple Music subscription service instead of purchasing a lot of music. That gives you access to a great deal of music and you pay a monthly subscription rate instead of paying for each individual song/album. If you lost your iTunes library, it may be a viable alternative. See this for information about Apple Music. Listen to music and more in the Music app - Apple Support

Because it is not part of the backup.

Backing up the music on your phone would be redundant and wouldn't accomplish anything other than chewing up unnecessary space since it is all either re-downloadable at no charge from the iTunes Store or can be synced back to the device from your iTunes library.

The iPhone is not a backup device or a data transfer device.

The iPhone is not intended to be a music storage device. Any music ripped from CDs must be stored elsewhere to guarantee preservation. The iPhone backup process has never backed up media files.