Hi Simeon, I assume you only mean for when cyanobacteria is alive. The only thing I found is this:

"In both prokaryotic and eukaryotic microbes, the role of polyP as a PO4 3- reservoir depends on the organism's capacity to take up PO4 3-, synthesize and store polyP, especially when PO4 3- is more abundant than is required for growth, and degrade it when the level of available PO4 3- in the environment becomes limiting (Orchard et al., 2010). This accumulation dramatically increases when organisms are preconditioned in medium deficient for P. Exposure to excess PO4 3- after this preconditioning leads to the “luxury uptake” of PO4 3-, enhanced polyP synthesis and accumulation in acidocalcisomes, which can serve as P and energy reservoirs. This phenomenon has been designated the “overplus” or over-compensation response and has been extensively studied in cyanobacteria (phytoplankton) and algae in ocean, lake, and river habitats"

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7332688/

Finding this a very interesting question after reading some more:

More to add: other than cyanobacteria mortality, cellular leakage is another way that phosphorus can be released into the environment.

"... the activation of phosphate uptake systems is facilitated by DIN supply in N-deficient non-N2-fixing cyanobacterial populations. The reactivation of phosphate uptake systems occurred within 24 h after DIN input, and, based on the high uptake rates (LP) determined here, the acquired phosphate needs to be immediately transformed into polyphosphate reserves in order to avoid cytoplasmic osmotic problems and phosphate leakage from the cells (Plaetzer et al. 2005). "

So I assume that you may need to look at factors which affect such P leakage rates.

https://academic.oup.com/femsec/article/95/2/fiy229/5195515

Some other leads into the ways in which nutrients including P may be liberated to the environment:

".... through processes as diverse as cellular leakage or viral lysis (Healey 1982, Istvanovics et al. 2000), parasitism by bacteria or fungi (Paerl 1988), decomposition of detached filaments and dead colonies (Healey 1982), and grazing by herbivores (Fey et al. 2010). "

https://esajournals.onlinelibrary.wiley.com/doi/10.1890/ES14-00174.1

Hope this is helpful. Best of luck

Here a recent review article about poly P in cyanobacteria and algae:

Sanz-Luque, E., Bhaya, D., & Grossman, A. R. (2020). Polyphosphate: A Multifunctional Metabolite in Cyanobacteria and Algae. Frontiers in Plant Science, 11, 938. https://doi.org/10.3389/fpls.2020.00938

If your question is not sufficiently answered in there, consult its extensive bibliography.

Hi all, do pardon my late reply.

Sate Ahmad: Thanks, I have read before some of the references you mentioned, which weren't what I was expecting (I was looking along the lines of a PO4 release response under different stressors). From your train of thought, I found another paper which mentions the release of PO4 from a cyanobacterial species due to the breakdown of its capsular polysaccharide and subsequent mucilage sheath disaggregation, which technically answers the question:

Article Phosphorus release from cyanobacterial blooms during their d...

Thomas Petzoldt: This paper is actually one of my main go-to references whenever I need answers. Unfortunately, it concludes with the same question which I am asking. Although while reading further, I stumbled upon an interesting paper (although EBPR-based) which concluded that Mg2+ ions somewhat inhibited anaerobic PO4 release, while increasing pH stimulated PO4 release. This is however not cyanobacteria-specific.

Article Biological Phosphate Uptake and Release: Effect of pH and Ma...