AirPort Utility, Apple’s official app for managing its AirPort wireless appliances, has received an update fixing bugs that caused many issues for iOS 13 customers, including unexpected quits.
Version 1.3.6 of AirPort Utility for iPhone and iPad includes general stability and security improvements, according to release notes accompanying the download.
I can confirm that this update has resolved the iOS 13 compatibility issues. I can now use AirPort Utility without any hiccups whereas the previous version would abruptly quit after entering a password for one of the listed AirPort devices.
The previous AirPort update, released in August 2018, brought AirPlay 2 support to the 802.11n models of the AirPort Express base stations. Apple no longer manufactures or sells AirPort-branded products, but continues providing compatibility fixes and basic support to owners.