I received backdated unemployment benefits in 2021. I was paid in 2021 but my claim dates back to Nov 2020. Do I claim the unemployment income now or next year?

Did the state issue a 1099G to you for 2020?  it would seem very unlikely that they would do that---but make sure.   You should more likely get a 1099G that will go on your 2021 tax return.

https://ttlc.intuit.com/community/entering-importing/help/how-do-i-report-unemployment-if-i-didn-t-get-a-1099-g/00/26866

I haven't received a 1099-G yet, also not available online. I assumed this was an error at first. Now I'm thinking that it will happen next year. However, I haven't been able to find anyone that can actually confirm this for me. 

Thank you for the article link!