Cash out refinance - do I report the outstanding principal on the original 1098 or the new principal with the higher balance from the new lender's 1098?

Report the outstanding mortgage principal balance on the "new" 1098 - the one you received on the refinanced mortgage. Leave Box 2 of the "old" Form 1098 empty (or enter $1 if"0" or "Blank" won't work).

The original 1098 would not have had an "outstanding mortgage principal balance" at the end of 2020, even if the 1098 shows an amount in Box 2. When you "refinanced" that loan, you paid it off completely. 

If you have to make an entry in Box 2 of the "old" 1098, don't worry. This will not have any effect on your tax calculation and will not generate an error in either TurboTax or with the IRS, From an economic perspective, it is accurate - you owed virtually nothing on this mortgage at the end of 2020. 

There are many places in TurboTax where you must make a non-zero entry, primarily to let the program know that you answered the question and that the answer makes some sense.  

In this case, entering "$1" tells the program that you didn't forget to answer the question and that you had at least some amount of a mortgage loan balance to justify claiming an interest deduction.