I tried with my LG G6 phone which has a manual camera mode. The white balance is given in ºK. Unfortunately it’s quite off. Tested against my best known light with an Arrow XHP50 5000ºK 95 CRI and matches at 3800 º. Tried with an XML-2 4400º K and again was way off ~ 3200º. So there would need calibration to work depending on camera sensor.
Sure would like to try with a newer Sam phone, supposed to be better optics and sensor.
Thinking loud: One could take an older digital camera (RAW mode enabled), remove the Bayer Matrix, and take a shot of the beam after going through a prism (large distance between light and prism). Now you have the spectrum in terms of grey values, ready to be analysed by Image/J or other image processing software. Anyone tried this?