What is the legal responsibility of insurance companies to be forthcoming about repairs?

If I understand your question properly, it's understandable why others didn't quite comprehend it.

I believe you are referring to when one has a loss, and makes an insurance claim, what happens if the insurer controls the repair process and underpays the repairs and as a result you have an improperly repaired property which may lose value (diminished value), requires costly re-repairs and causes for further out of pocket expenses such as substitute rentals, temporary living quarters etc.

It is reasonable that should an insurer fail to properly indemnify you, where coverage is applicable and you have properly submitted your claim and proof of loss, and met with all policy provisions, you would have legal recourse under a breach of contract issue for the harm and damaged caused by the insurer's actions, or lack thereof. Some restrictions may apply such as contracts/policy provisions which may have ACV (Actual Cash Value) coverage vs. Stated Value Policy (a agreed upon fixed dollar value) etc.

Bottom line, the insurer has a contractual duty to provide you the coverage you secured, anything less and they enjoy undue enrichment and have failed to meet their contractual and fiduciary responsibilities to the policy holder.

Caution, there are no obligations to mandate that an insurer advise you of what you may be entitled, but once asked, they must be truthful.