After an engine change, we (mechanics) do a full power engine run to check the whole engine, parameters, but also systems connected to engine (generator, bleed,...). If the fan blades were removed/replaced/reshuffled we also compute the balance weight that has to come into the spinner and do a vibration test. That's all. If all within limits, safe to release to normal service.
If ,however, a certain parameter is not ok, we spend a long time on the engine ground run, which can burn a lot more fuel than a 2 hour flight, due to the testing at max power.
On the aircraft I work on there are over 16 differnet engine tests described in the MM. For example high power, part power, idle run leak check, health check, vibration run,...