The Project file does not contain any music It contains the path and filename to your music tracks. Somehow, iMovie is not able to find the music tracks at the location where it thinks they should be. You may be able to hover your mouse over the yellow warning sign and see the path where the music track is expected to be.
If anything is in a different place, that would explain it, but normally, when you restore from Time Machine, everything should be back where it was. If you loaded or moved the music tracks after your last Time Machine Backup, that could explain it.
The easiest solution might be to delete the music tracks and drag them in again.