No. Only income received in 2018 is entered on a 2018 amended tax return.
This is incorrect. There is a specific spot where it asks, "Federal Income Tax Refund received in 2020 for tax years 2019 or prior years".
Did you itemize deductions in 2018?
If you did itemize in 2018, include this refund as income on your 2020 federal return.
If you did not itemize deductions in 2018, you do not report the refund on your 2020 return.