Unemployment refund

So I filed my taxes 02/11/2021. After that, I received another 1099-G from my state. The first one the sent in January apparently was not accurate.

 

I never amended my taxes because I didn’t think it would be a huge deal. But now with this unemployment refund, I’m starting to wonder. 

should I have amended my taxes? Is the IRS going to be going off the first amount I put in my taxes? Or would they have received my updated 1099-G from my state?

 

Basically, my question is, should I amend my taxes or not? And how can I tell if they will be sending me a refund?