new insurer asks about damage history from recent years what do I enter

Damage history is part of risk assessment

You report a claims history because the insurer uses it to determine the premium and terms on that basis, not because there is a separate reporting obligation in a law that specifically prescribes this. The question recurs in almost every quotation request for business insurance: liability, transport, cyber, fire. The insurer wants to know how many claims there have been in recent years, what caused them and what was paid out. That is the same logic as with the question about financial health: the insurer weighs risk against premium, and claims history is a direct indicator for that.

In practice, the questionnaire asks for an overview per policy year: number of claims, claims amount in euros, and often an explanation for claims above a threshold amount. The supporting document for this is usually a claims extract from the previous insurer, also called a "claims declaration" or "no-claims declaration". If you do not have that, your own policy administration with claims dates and payment amounts is the alternative. If a claims extract is completely missing, for example because the previous insurer no longer exists or does not respond, then "not available, explanation sent by email" is a realistic answer — an insurer is used to that in practice.

Where this comes from: insurance practice, not a statutory reporting obligation

There is no article in the cited sources that regulates claims notification to a new insurer; this follows from the way insurers accept risk, not from the Trade Register Act 2007, the Anti-Money Laundering Act or the CSRD. However, the subject sometimes touches the other side of the same file: an insurer asking about claims history often also asks in the same questionnaire about the structure of ultimate beneficial owners, because client investigation and risk acceptance come together in one intake process. That is a separate answer with its own source, and is separate from the claims question itself.