Data points for processing time for one child passport (his third but doesn’t matter), with expedited processing and expedited 1-2 day delivery:

Wed Dec 28: Dropped off at USPS post office / passport facility, Atlanta, GA.
Wed Jan 4: Check electronically deposited. (Check # 3530 (Converted ACH) PASSPORTSERVICES PAYMENT 230103 0330 PCTB02——000000)
Wed Jan 4 (same day): U.S. Passport Application Status website updated to show "Application Status: In Process" with an application locator number. Which didn’t really help.
Tues Jan 17 - "Application Status: Shipped" along with USPS tracking number.

Projected receipt date Jan 18 or 19 (USPS 1-day delivery might be goofed coming from Tucson)

Note - never received automated email even though my email was both on the application and I registered before and after they entered in the system

Total processing time from USPS drop off to receipt was 3 weeks; 21 or 22 days total, including two holidays (New Years and MLK).