In (cyber) space no one can hear me scream.

The COSHH Regulations have NOTHING to do with a manufacturer supplying a Safety Data Sheet for a substance or mixture classified as hazardous to human health or the environment. It is REACH Article 31 "information in the supply chain" which describes when an SDS must be made available.

You are right that COSHH requires an assessment of the substance or mixture as used however dealing with old contaminated sites requires specialist involvement determining what is present (not all hazards are visible / noticeable) and then developing an appropriate remediation plan.

As per your link the material is an effect of the works rather than something supplied or manufactured so it would be unwise to seek out an SDS for pure Prussian Blue as that may not be the total contaminant.

Ok ‘Billy Blue’ is a waste products found on  gasworks and similar sites. Its not toxic but definitely harmful and an irritant. Of course it does not come with an SDS. As it is not a product put on the market by a supplier, but a by-product left over from a historical process. The SDS is actually something that comes under REACH not COSHH. COSHH places legal duty on employers to manage the risk to their employees from any hazardous substances in the workplace, not just those bought in. Carbon-monoxide is similarly something created within the workplace ( by boilers or engine exhausts) and the duty to manage it is part of COSHH- it has a WEL.

For this you need to start from first principles and research the hazardous nature of this waste. Remember the billy blue  will not be a pure material but it is likely to contain other contaminants.