Reverse engineering the protocol of a BLE lamp to integrate it in HomeAssistant

I recently acquired a daylight lamp through a reward program from my health insurer. It is the Beurer TL100 Daylight therapy lamp, it has bluetooth and can be controlled by the Beurer LightUp app. I have HomeAssistant running at home and naturally wanted to integrate the lamp into my setup, so that I could control it via the Web.

During the development of this integration I used some help from ChatGPT.