Let me try: It helps to separate each event and go step by step.

"distributed 94K from a 401K and paid the tax"

The outflow is as distribution to the person, or as a direct transfer/rollover to an account brokerage or financial institution?

"Put the entire funds in a non-deductible IRA."

That was a conversion, if done in the required timeframe for Rollover. Or, this just happens to have made funds available to be contributed to the IRA under the new qualification, such as earnings from wages for that same tax year? Because you might be relating things that are not related nor dependent on each other.

"Took out the earned income and paid tax on it"

The taxable amount would be proportional to the basis of all Traditional IRA accounts. It isn't just the Earnings, but a ratio. Even if one entire IRA account is for Traditional pre-tax and the other is Traditional nondeductible, whichever you take from, the distribution/conversion is based on their combined total value. You cannot take one specific category of funds from a mixed account or even just the one account.

"now wants to take the 94K and contribute to a Roth."

Which is treated as a conversion, and is treated the same as the Distribution from the perspective of ratio (basis vs values in all sheltered IRA accounts).

"I am perplexed"

Here's what "backdoor Roth" typically means/requires:

You want to contribute to a Roth account, but do not qualify based on income limits.

You have no other traditional IRA accounts. You put the Nondeductible portion into a traditional IRA account and essentially immediately directly transfer to a Roth.

That's when there would be no taxable anything to report.

That may not be what you describe here, @Ruth1