Changes to HA not automatically appearing in HomeKit

When transitioning our Phillips Hue bulbs to be controlled by a ConBee II stick instead of the Hue Bridge, after removing a bulb from Hue and pairing it with HA directly, the changes would not show in HomeKit on my iPhone. The changes would only appear after unpairing and re-pairing the HASS Bridge in HomeKit, which would result in me having to reassign the devices to their rooms again.

HA is running in a Docker container on an Intel NUC11PAHi5 running Ubuntu Server 22.04.
Screenshot 2023-01-31 at 10.32.02 AM|578x318