Once again:

They have a Sched C for 2021, if they got this money in 2021, because this is Business Income.

Like regular business income. Which makes it the same as business income. Because it is Business Income. The same as Doing Business and getting paid.

Which means it is subject to SE tax.

It goes on Line 1 for the Sched C, where you put business income.

The Client needs you to include Sched C, because this is Business Income.