Until it's forgiven it is a liability on the balance sheet. Once it is forgiven, it is nontaxable income and goes on the M-1 and in OAA.

I'm doing an amended 1120S return for 2020 due to the ERTC. The client received PPP forgiveness in 2021 for draw 1 taken in 2020. Should I amend the return to show the PPP as tax exempt income or wait and claim it on 2021 return?

I'd wait. At 12/31/20 it was still a liability.