"Property tax on your main home_____" - this refers to your main residence from Jan to Sept in 2019 AND to your new home from Sept 2019 to Dec 2019.
You possibly had two different tax bills for 2019 for your "main home"; if so, add them together. Note that you will have to examine the closing papers (or call the title company) to see if at closing, you ended up paying for those months (and not that the buyer paid for some of it on the new house).
Any property tax that was assessed on your old home while it was a rental property should be reported on Schedule E as a business expense (and NOT Schedule A).
Because of this split year situation, it becomes a bit convoluted, because property taxes are generally paid annually. On your old house (the one that become a rental property) you may have to manually prorate the amount of the property tax paid on your old house so that 9 months goes to Schedule A and 3 months goes to Schedule E (or however you allocate it).
Whatever you figure there for Schedule A, then you add any property tax paid on your new house for 2019 (if any).
And Schedule E should have the property tax allocated to the time (3 months?) that the old house (now rental) was "placed in service" (i.e., available for rent, whether or not it actually was).
There may not be a way to automagically enter this unusual situation in TurboTax, but if you will figure out the amounts by hand, you should be able to manually enter the amounts so that the numbers on Schedules A and E turn out correctly.
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