Data point. Sent to the US embassy in Bern, Switzerland:

Mailed: 8 June
Received at the embassy: 10 June (no further correspondence then or afterwards)
Issue date: 13 June
Postmark on return envelope: 17 June
Received Next Gen Passport: 20 June 22 June (checked the tracking number on the envelope, with A post it _should_ have arrived on 20 June).

Expired passport was in self-addressed stamped envelope with new passport. While I had provided postage for registered mail, it was only sent A+, which apparently included a tracking number which I never was informed of. Passport has 50 pages, which I will likely not use more than a couple as I only travel with the US passport into the USA, as I'm a dual citizen of USA/Switzerland.

The only hint I had that the passport was in work was the message the Mobile Passport Control App sent me. I couldn't read it as I had forgot my PIN. :-/