Analogously, think of memory management in a computing context. You have a program running that gradually allocates memory linearly over a certain time period (daytime), but then releases all that memory linearly during another time period (nighttime). Say you're dealing with 4GB of memory and you run the memory-increasing part for 6 hours, then run the memory-decreasing part for the next 6 hours, and so on. Suppose you never allocate the full available 4GB when you're dealing with a 6 hour on/off timecycle (the rate of memory allocation is too low to get to 4GB in 6 hours) - but what happens if you extend the timecycle? There's some timecycle length at which you will finally attempt to allocate more memory than the 4GB your hardware is capable of, so the host OS starts swapping or writing stuff to disk to deal with the excess.
Biological systems don't have a "host OS" that regulates their molecular byproduct management though. Extra atoms/molecules are just going to escape into the surrounding environment. Perhaps the oxygen buildup during the daytime might have worked this way with the cyanobacteria - longer days led to more oxygen being produced than could be physically retained in the immediate vicinity of the cyanobacteria (some type of saturation effect), so all the oxygen in excess of the saturation threshold effectively "escaped" and became unavailable for metabolic "re-consumption" at nighttime. Thinking about the longer nights that accompany the longer days, there's probably a period of time in these longer nights during which all the "nearby" oxygen has been fully consumed, and the cyanobacteria more or less sit idle.
Oxygen saturation in the surrounding environment seems like the missing logical piece from this popsci article.
Mind, I've generally found the Great Rusting narrative to be fairly convincing: all the highly oxidised rocks on Earth's crust quite likely didn't arrive on the planet in that form, and picked up free oxygen as it was introduced to the atmosphere, effectively buffering the new addition. Though perhaps a slowing rotation did help reach and flip the tipping point of the Great Oxygenation Event.
Reliable witnesses from the period are hard to find.
The opposite effect is expected during the daytime: as temperature increases, reaction rates go up exponentially until they saturate according to the limiting resource. This could still mean producing much more oxygen in the daytime than can be consumed during the period of torpor at night.
Blue-green algae are aqueous. Diurnal temperature changes in even reasonably shallow bodies of water are fairly minimal.
Early Earth had much lower solar insolation than today (by about 25%), though an atmosphere largely comprised of greenhouse gasses (CO2, CH4). That would probably have also had a levelling effect on any short-cycle termperature variation.