"and CPA advised client to sign up with ADP and run her own (single person) payroll in Dec 2021 to save on SE taxes. It's been very "informal" from what I can tell."

So now we know that anything from/regarding that CPA cannot be relied on. That is Basically a bad statement. You cannot pay yourself through Payroll from your own LLC. You have no SE taxes as an employee of the S Corp. That is confusing two different provisions, and payroll is a basic, fundamental, thing for a CPA to know. And no one "saves" on SE taxes. They become Employer + Employee taxes; they are shifted, not saved.

"I don't believe she has elected S Corp status yet but has done 2021 one-time/single payroll as if she has following her CPA's guidance. New CPA told me (in 10/2021) he would elect S Corp status when he files her taxes for 2021, but unless an exception applies, I didn't think she could do that"

I thought you were filing her taxes.

Well, here we are at the End of Feb 2022:

To elect an S-corporation taxation entity for your business, you must submit IRS Form 2553. This must take place no more than two months and 15 days after the tax year that you want this change to go into effect

What a mess.

Perhaps you should unwind 2021 payroll, file for S Corp election for 2022, and start payroll for 2022?