This is such a huge subject that you can spend a decade at university learning business management and project methods only to find out that nobody knows how to measure productivity in a universal way. This does however not prevent people from trying, and usually failing.

For jobs like therapists you can try to measure productivity by measuring how fast patients stop requireing theraputic help. There are a number of factors you can measure such as the amount of perscribed medication (these cause side effects and kill the liver), episodes of psycotic breakdowns, how effective the patient is at work and at home, etc. But as you might imagine these numbers can be completely wrong in many cases. Not all therapists see the same type of patients so you will see very different performances. Some therapists might optimize for these metrics in a way which end up hurting the patient in the long run.

For bus drivers you can measure how often they crash (most full time bus drivers have about two minor crashes a year), you could ask the passengers, or just record complaints, you could measure how accurate they are between stops, some measure the acceleration on the bus trying to get the peaks as low as possible, you could measure the fuel consumption, etc. All of these are possible but again different drivers prefer different routes and will therefore perform differently according to these metrics. And you have conflicting metrics such as low acceleration rates penalizing emergency braking for safety, or making drivers run red lights to keep the time table.

Teachers are usually measured by standardized tests. All the pupils in the country take the same test which means you can compare the teachers and schools. But as soon as standardized tests are introduced it demonstrates social inequality in the sociaty and is also ripe for manipulation by the schools.