Bluetooth is only really an option for Apple, not any iOS developer. Slightly different for Google, where Android lets background apps use Bluetooth. So no country has tried to use bluetooth in their apps. Other than South Korea it sounded like contract tracing had been abandoned.
In South Korea, I suspect that the big difference is the specialist tracing teams they are using combined with the random testing of the public to find new potential sources really quickly. I am sure the app helps but it is probably not the route to normality. It requires thousands of contact tracing teams and high amounts of random testing on very low numbers to work, it is a small piece a combined set of policies that work together.