(Among other consequences.) https://www.cdc.gov/habs/environment.html
From that Wikipedia item,
"Each iron atom converted at least 13,000 carbon atoms into algae."
https://www.dw.com/en/artificial-whale-poop-could-save-the-p...
and burning Australia is a proven way to generate more plankton. https://nicholas.duke.edu/news/australian-wildfires-triggere....
One hypothesis is that algae are limited by some single resource which could be gradually dropped out the back of cargo ships as they cross oceans, seeding carbon-absorbing algal blooms as they go.
(I heard about this nearly 20 years ago, so I assume that has either been tested or banned since then…)
As mentioned in a sibling comment, it could run on some other heat source, but that hasn't been demonstrated yet on the scale of agriculture.
Terrestrial ag fertilizers don't have to be produced by fossil fuels.
The Haber–Bosch process used to make ammonium nitrate can be solar powered instead of using methane.
Phosphate rock processing could greenified for a green "green" phosphoric acid wet process.
Potassium from potash is mostly a passive solar evap process.
For seaweed aquaculture, iron sulfate is used because iron availability is the most frequent limiting factor. It's frequently a byproduct of steel production, in much need of greening itself, and produced in large quantities. Volcanic ash is another abundant source.
Keep in mind the vast majority of agricultural yield growth the last century is giving these limiting nutrients as fertilizer for plants, so it is successful and worthwhile for land based farming atleast.