Update!

7/22: Passports arrived today via Priority Mail! I'm surprised it came this early since I just got the notification yesterday that it was 'Approved.'

Historical Timeline:
4/20: Passports sent by Priority Mail for routine service
4/24: Arrives at mailing center in Irving, Texas
5/19: At around 8 pm Pacific time, I received emails notifying me of a status change from 'Not Available' to 'Processed,' with a message saying they are currently processing in 10-12 weeks.
5/20: The checks were cashed.
7/21: Received an email that my passport status is now 'Approved' and is expected to arrive by July 27th.