In iron sulfate fertilization you're only adding two nutrients (iron and sulfur). Now that nutrient is in excess in one area so metabolic uptake of all nutrients increases locally, creating a concentration gradient that reduces nutrients available elsewhere. This leads to one of the other limiting nutrients like phosphorus or nitrogen preventing growth of other life forms in another location since the concentration gradient created by the phytoplankton sucked it away. Also sulfur concentration changes metabolic pathways through epigenetic effects so there are other effects just within the phytoplankton that depend on the species that happens to be present that will determine what the exact concentration gradient would look like. The dynamic of nutrients shifting of the metabolome makes modeling and risk assessment difficult since some species are known to produce toxins which can bioaccumulate. https://en.wikipedia.org/wiki/Phycotoxin

Not sure if it's a time to cry about the loss of a bush of roses when the forests are burning. Any natural iron supplementation like blowing the dust from Sahara or a river carrying out to the ocean waters full of red soil should be causing similar effects. Granted, rivers are likely carry other nutrients, often in excess, but this also does disrupt what grows or not in the surrounding areas.

Iron fertilization may still be pointless since the effectiveness is being debated afaik. On the other hand if it does work well for a competitive price compared to other methods, I would rather have a fish in the middle of the ocean full of algal neurotoxins and lower global temperature than the same fish cooked. No need to at it though.

Adding sulfur as a nutrient to the ocean is unlikely to have much effect, as seawater already contains about 3 ppm sulfate, thousands of times the concentration of iron.