I’ve been told that many cot mattresses give off toxic gasses and to buy purely organic mattresses instead. Do you have research about this?

Red Nose recommends that all mattresses for baby need to be firm, clean, well-fitting & flat.
https://rednose.org.au/article/what-is-a-safe-mattress

Some bedding products have been developed on the basis of a theory proposing that toxic fumes are emitted by cot mattresses and may be associated with SUDI deaths.
However, SUDI researchers and paediatric experts consider that there is insufficient scientific evidence to support this theory.
Red Nose strongly disagrees with the theory as it is unsupported by the evidence.

Red Nose recommends baby sleeps on a firm, clean, well-fitting mattress that is in good condition to reduce the risk of SUDI and fatal sleep accidents.
https://rednose.org.au/article/no-evidence-to-link-toxic-gas-from-mattresses-and-sudi