Finally got this working and my Rachio is finally talking to Home Assistant over HomeKit.
This post cleared everything up.
The settings for everything are saved to Rachio’s cloud service. You just need to hold the stop button to factory reset, wait for the amber light, go to the controller settings, update wifi, and add it back. From there, you can initiate a HomeKit connection again. Nothing will be lost except for the reliance on Rachio’s cloud service to control your device.
It sucks that there’s no timeout for the HomeKit connection, but I’m glad that I finally got it working. Even though it took me 5 months to get around to doing it.