The bank does not have delegated underwriting authority and completes a one-time close (construction/perm) loan with prior approval from the investor for purchasing the permanent portion.
Additional facts: The bank will keep the construction phase in house until completion of home and then modify the loan and sell it on the secondary market.

Who reports this? Is this HMDA reportable on the bank or investor's LAR?

Construction loans are not reportable. The investor will report this when they purchase the loan.

The investor made the decision, it's their reporting.