I think when people talk about burn/embed they’re probably talking about the BWF/BWAV ISRC that’s added to WAV files, not MP3, and is a standard. That can be done in Wavelab Pro or Sonoris ISRC Editor.
https://www.mpg.org.uk/category/mpg-blog/campaigns/isrc-in-bwav-files/
Not sure why they call it burn/embed because it can be modified, but they do.