I married in 2020. Last year we filed separately, she itemized, I took standard deduction, should I say we took standard deduction or itemized in 2019?

I would go with standard (if you are the one filling out the forms).

Pick whichever deduction method - standard or itemized - was used by the spouse with the highest 2019 income  (although it is unlikely your answer here will change your current year's tax calculation in any significant way).

The only reason the program may be asking you this is if your spouse (who itemized) deducted state income tax last year and then got a state tax refund in the same year. The refund would be taxable income for 2020. If your spouse itemized last year, it is more likely that she had more income than you - selecting "itemized" as the answer is more likely to have the program treat a state tax refund correctly.