Never mail anything as a bunch - there is too much of a chance of one or more of them being overlooked. If you mail send them each individually and I would send certified/return receipt, so I know when the arrived.

If you send 2021 in before 22 and 23 there is a good chance that they will just issue a refund check - if you want 21 to cover 22/23 then they have to be processed first so the IRS will "hold" or "pull" the 21 refund to cover. maybe. possibly

I think you need to think of each year as stand-alone - I would mail 2020 & 2021 now and then when efile opens late January efile 22 & 23. I would have client make the payments due and then just get the refund back. I would not count on the refund, what if you find out that somehow they did get stimulus checks already.