I'll add a data point:
April 6th: Sent my application for expedited renewal via priority mail
4/9 USPS Tracking shows delivered in Philly
4/10 Passport status site shows my application was received and under review
4/17 Status is "approved"
4/19 New passport received via priority mail. Passport status still shows as "approved". So just under 2 weeks from when I mailed the application.
I requested email updates of renewal status but never received any.