"As of now, I put $6,000 under "IRA basis for 2020 and earlier years""

Put, where? A 2020 contribution is a 2020 event, even if made in 2021. It goes on the Tax Year 2020 paperwork. The Form 5498 for 2020 will show it is for 2020 and will show $6,000. If not, your taxpayer did it wrong.

"and $6,000 in the field "2021 nondeductible contribution (-1=none)""

You cannot work with 2021 until you address 2020. Let's go back to this part: "Are you able to contribute $12,000 (for a two year period) for a backdoor Roth?"

Let's lay out how it should be, and I will make assumptions based on what you told us. If they are wrong, this isn't your answer, then.

For tax year 2020, they do not qualify for Roth Contribution. And they determine 2021 will look about the same. Instead of putting $6k into Her IRA and $6k into His IRA, they determine he should put $6k into his for 2020 as nondeductible and another $6k right now, early in 2021, intended to be for 2021 also as nondeductible. Assuming there are no other IRA/SEP/SIMPLE before that money is contributed, then the $12k is basis (post-tax) and is immediately transferred or rolled to a Roth account, which means it also avoided Earnings (which would be pre-tax).

"Backdoor" simply means Conversion.

And the tax filing of 2020 is supposed to have the 2020 contribution on it. There is no Transfer/Rollover event in 2020 and no Conversion. The contribution is documented.

The Tax filing of 2020, then, establishes an account balance as of Dec 31, 2020 + the tax year contribution paid in before the tax form filing due date.

Now it is 2021:

The contribution Form 5498 for 2021 will show up later, that's true; you would have a proof of deposit, a statement, something to prove there is $6k in as 2021 ("Current Year").

There is a 2021 1099-R for the $12,000 Distribution that is the Transfer/Rollover of Basis to Roth. Because it is Basis and there are no earnings in the account, this is only basis, and that makes it tax free (already taxed, really). That was the full amount that went in, and came out. No withholding.

Having a Conversion of $12k isn't a problem. It's the amounts and timing and identification for what went into the IRA that needs to be addressed.

You need to amend 2020, it seems. This is assuming the amount(s) into the Trad IRA met the deadline(s), of course.