Recover a dropped MySQL database with its procedures
If you are lucky, you won't need the backups.  (Oops, you have already gone beyond this step.)

If MySQL's data directory was left behind by the uninstall, then simply reinstall.

Was the backup taken using mysqldump (either explicitly, or under-the hood)?  If so, perhaps it failed to have the arguments asking to save "stored routines", etc.

I fear you are out of luck.