It appears my passport was just approved! Timeline:

4/19: Applied in person at a courthouse in Florida
5/19: Email from DoS showing application "In Process" as of the day before (passportstatus.state.gov also updated a day late)
7/22: Email from DoS showing application approved

The U.S. Department of State approved your application for your passport book and card. We're now printing your passport book and card and preparing to give it to you.

You requested routine service when you applied, which we are currently processing within 12 weeks. You should receive your passport book and card on or around 07/28/2021.

I did NOT pay for expedited service; however, I did reach out to my Representative's office, as I had heard they can help speed things along. While the message says I should receive my passport book and card on 7/28, my Representative actually sent me back a tracking number showing that it was mailed out on 7/20 (two days before the approval notice) and will arrive on 7/23 (five days before the estimated arrival time.) What's also interesting is that it's coming from Arkansas, even though my locator code indicates New Hampshire.