If I'm taking the standard deduction, is my 2019 state refund taxable? If it is taxable on which line should it be included?

If you took the standard deduction in 2019, then the state tax refund related to tax year 2019 that you received in 2020 is not taxable and does not need to be reported on your 2020 federal state return.

Having taking both federal and NY state standard deductions in 2019 and received a 2019 NY state tax refund, is this refund taxable on the NY State 2020 tax forms - I did not receive a 1099-G reflecting that for 2020. Would I have to add that as an Other income or consider it as non-taxable?

Since you took the standard deduction in 2019, your state refund is not taxable.  You do not need to enter this anywhere.