There is one way to make the online version correct.
1. Enter 0 in box 2 for 1098, except for the original mortgage
2. After entering the 1098s, click "Continue". At the "Let's wrap up your mortgage interest deduction" screen, for the original mortgage, in box "Enter your loan balance as of January 1, 2021, or the final principal balance if you paid off this loan in 2020.", enter the balance of the final refinance mortgage at the end of the year (12/31/2020).
This will cause TurboTax to
1) only account for balance of the original mortgage and not any refinance(s)
2) compute the average mortgage balance correctly with formula (beginning balance + ending balance)/2.
The deduction works out as expected compared to hand calculations. I also downloaded the worksheet to double check the calculation. In my case the mortgage that was refinanced in 2020 originated before 12/14/2017, and in the worksheet it shows 0 for mortgage balance after 12/14/2017 and the correct amounts for before 12/14/2017.
This is basically equivalent to overriding the average mortgage balance on the desktop version.
