Contact tracing is a valuable tool when eradication is an option. It probably should have been used early to manage the current H5N1 (bird flu) pandemic by tracing poultry and livestock movements. Can't do much about migratory wild birds, but we should be able to manage people spreading it.
Problem is vaccination doesn't necessarily prevent transmission for respiratory viruses. There's a general misconception that being vaccinated will prevent you catching it - like you have some invisible shield.
Vaccination should prevent it progressing from an upper respiratory illness to lower respiratory where you primarily develop pneumonia (Covid triggered all sorts of other immune inflammation responses and affected other organs). Most vaccine injuries were the same immune response, but could have been worse had the individual caught Covid.
What vaccines don't do is prevent you spreading a highly transmissible virus before your immune response kicks in and deals with it.