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You are correct, you should have gotten the tax credit for unemployment paid for 2020, on your 2020 tax return.

In general,  unemployment benefits are included along with your other income such as wages, salaries, and bank interest.

For the tax year 2020, the first $10,200 of unemployment income was tax free for taxpayers with an AGI of less than $150,000 regardless of filing status. 

This "credit" was only available for the 2020 tax year. It does not apply to unemployment income for 2021.

This was only available on the 2020 tax return. It looked like this (it was reported on Schedule 1):

Click here for additional information about reporting unemployment benefits.

Click here for information on the 2020 Unemployment Compensation Tax Credit.