Unemployment and 1099G

I qualified for PUI (pandemic unemployment) in 2020 and 2021 but did not receive any benefits/money until 2021 for both 2020 and 2021 because the unemployment offices were so backed up on paperwork. It all came in one lump sum in March 2021 .  I received $10,224  on 3/3/2021 but $4446 of the payment was for 2020.  I have not received a 1099G.  Do I claim the unemployment benefits for both 2020 and 2021 on my 2021 tax return since I received all the money in 2021 or do I claim the amount I was suppose to receive in 2020 ($4446) on my 2020 tax return?   In addition, if I have to claim it all in 2021 since that is when I received the payment, will I still get the federal tax advantage of not having to pay taxes on  $10,200 UI (Tax waiver/American Rescue Plan)?   I have not filed my tax returns yet for 2020.  Please help - I cannot find any answers anywhere about these two questions.