Original loan was temporary financing to purchase and improve property. Now the loan has been refi'd to permanent financing with additional takeout for overrun improvement costs.

I think this should be home improvement purpose, b/c of the takeout to cover the additional improvement costs.

Since it was not construction to perm, it would not be purchase; and since there still are some home improvement considerations, it would not be refi.

Is this correct?

I would report it as a purchase. If you didn't report the first loan and called it temporary financing, this would be your purchase loan.

Per appendix D of the Guide: "A home purchase loan includes both a combined construction/permanent loan and the permanent financing that replaces a construction-only loan."

A light bulb went off...

Because it was temporary financing to purchase then the permanent financing of the purchase is considered purchase

same as construction to perm.

Right?

I would agree with that.

I would agree. It appears you have not yet reported your "purchase" for this loan, so this would appear to be your purchase.