You can still try to estimate this using something called QALYs which are life years adjusted for quality of life.

A breast cancer scare, is certainly harmful, but it's important to remember that it is going to be a short episode as it becomes clear that the tumor is not growing. So you have maybe a few months of scariness.

On the other hand cancer is brutal, and death is permanent. Years of life cut short. The years leading up that are extremely sad. The impacts of death extend beyond the person to their family and friends.

When people try their best to measure these things on balance, breast cancer screening is overall a good intervention.