I've some news, because I'm able to tell all of you where the temperature reading in the app should be coming from (my new light came in so I could check out the circuit of the led cluster).
Therefore I could conclude that the temperature sensor isn't on the led cluster, but it should be U8 on the main PCB, which means it measures the temperature next to the ESP (the used ESP version doesn't have an build-in temperature sensor). Which type of sensor U8 is exactly, is still unknown, I will have to see if I can find out using an oscilloscope, my current guesses are a one-wire type like ds18b20 or an i2c type.
In the part in the housing where the mainboard is located, there also is no airflow, so the temperature difference won't be as big as on the led cluster or heatsink.
Therefore, in my opinion, the only way to make sure if adding thermal paste works, is measure the temperature of the cluster before and after pasting using an IR thermometer/camera (or stick another temperature sensor on there).