Here's the timeline I just experienced for passport renewal this Spring.

tl;dr Mailed out on March 16 (via Canada Post), renewal of an emergency passport, regular / not expedited, marked as mailed back on May 25 — exactly 10 weeks after initial mailing.

I'm a US citizen living in Canada, and this might be useful for others in similar situations.

1. In Summer 2022, I got a one-year limited-validity/emergency passport from a US consulate thanks to advice in this thread; due to various immigration and travel constraints, I hadn't been able to do a normal renewal.
2. On March 16th (2023), I put my limited-validity passport in the mail (via Canada Post) with the DS-82 renewal form; no fee is required for replacing an unexpired limited-validity passport with a full-validity one.
3. Within days after I had mailed it, the State Department bumped its Routine Processing time from "8 to 11 weeks" up to "10 to 13 weeks"… urk 😳
4. On March 30th (14 days after mailing), the Passport Status page site marked my application as "In Process"
   • Locator number 35
5. There were no updates to the status until May 25th, and I was repeatedly unable to reach the National Passport Information Center due to high call volume.
6. In the meantime I travelled back and forth to the US twice (by land… can't fly without a valid passport or Nexus card).
7. On May 23rd (68 days after mailing, 54 days after "In Process"), I contacted my Congressional representative’s office, explaining my summer travel plans and passport processing delays. They promptly got back to me, but with a somewhat formulaic response, mostly just offered to help me figure out how to make the payment to expedite it.
8. On May 25th (70 days after mailing, 56 days after "In Process"), the Passport Status page changed to "Mailed via US First Class Mail"… whew 🙌
9. On June 2 (78 days after mailing, 64 days after "In Process", 8 days after "Mailed via US First Class Mail"), I received the new passport.

I have no idea if contacting my Congressional representative’s office helped or not, but I'm glad I did it.