If one spouse is self-employed and the other is employed (w-2), what is the deadline for the 2021 return? Is it 1/31/22 (deadline for self-employed) or 4/15/22?

There is no separate deadline for paying your taxes if you are self-employed vs a W-2.  

Estimates are due on the 15th of the month (each quarter...) not the 31st.

And if those estimates were not paid earlier this year, there may be penalties for late payment (unless there's a farm involved - they have some wonky deadlines).

Or not (penalties...) .... depending on a lot of different variables.

I think you are confusing functionality and tax form. Form 1040 has a due date of April 15 (more or less) and a Self-Employed person filing their business tax info on a Sched C will then be including the Sched C, as a Schedule, to Form 1040.

A Self-Employed person working for their partnership would be filing their business tax info on Form 1065. Notice that Form has some of its own Schedules, but the Form is specific to the entity type.

And Form 1120 is for a C Corp.

And Form 1120-S is for an S Corp.

Your "self-employed" person might work for their own corporation as a shareholder-employee, and notice these tax forms have the different due dates than the Form 1040.

Pay attention to Due Date by Form.

"The self-employed person has not made estimated tax payments for 2021, so will be paying for the full year."

Did you know that isn't the right perspective? The 1040-ES is for the tax payer(s)' entire financial picture that is projected for the 1040. It isn't just the business. The people are supposed to meet the requirement based on the 1040. Not because one is self-employed. The self-employed person could even have a loss, and yet the household could be penalized for not making estimated payments because of investment earnings and other activities.

And an easier way to do what you seem to be describing is to have the employed person increase their W4 withholding. Example:

John is an employee and has $100 per week deducted towards Federal Income Tax. Sally is self-employed and at the end of the year, they discover they should have paid by estimate another $5,000. Let's use that year's taxes owed (not balance due) info for the next year's projection and have John set his withholding to meet Safe Harbor.