Why would the amount shown on Schedule 1 under my state refund the year before be doubled what I entered?

if you used TurboTax for 2019, the refund was already proforma'd into the 2020 return. thus your manual entry ended up doubling the refund. 

I can only guess that you transferred 2019 into 2020 and the refund amount transferred, then you manually entered the same amount again.