Do you already know this thesis? It is a great overview and provides some band math methods to correlate cyanobacterial bloom with satellite images:
Remote Sensing Models of Algal Blooms andCyanobacteria in Lake Champlain
Also a very good article using band ratios: A 30-Year Assessment of Phytoplankton Blooms in Erhai Lake Using Landsat Imagery: 1987 to 2016
I have no idea about the spatial extent of these blooms in your study area but they should at least be coverable by the spatial resolution of the bands suggested in the studies. Some bands of Sentinel-2 are 60 meters only, so you might have a problem with mixed pixels.
This presentation underlines the need for careful radiometric calibration: Assessing the ability of current and future Landsat missions to monitor cyanobacteria blooms using modeled spectra matching