We have a customer refinancing a commercial purpose loan using their primary residence as collateral and getting additional funds for another commercial purpose. Can this be treated as a commercial loan, or do we need to treat it as a cash-out refinance subject to RESPA, HMDA, ATR, etc.?

Assuming you are satisfying and replacing an obligation secured by the dwelling it would be reportable as a refinancing for HMDA. However it's a business purpose loan so RESPA and TIL will not apply.