This is an Homebridge add-on for Home Assistant. Homebridge provides a lightweight HomeKit API implementation with plugin support.
Note that Home Assistant supports HomeKit natively these days, both as a controller and as a device, so you probably don't need Homebridge if you just want to integrate with the HomeKit ecosystem. However, Homebrige has a lot of plugins, so it can still be useful to bridge some less-supported devices (e.g. Nest) into Home Assistant.
Add the add-on repository and install Homebridge from the add-on store.
To configure Homebridge click on OPEN WEB UI from the add-on page.
This add-on was inspired by adsb-multi-portal-feeder to leverage a pre-existing Docker image and integrate it into an add-on (Docker Homebridge in this case). The add-on icon is derived from Material Design Icons. These projects (and Homebridge itself) deserve all the credit here. This add-on is unrelated to the deprecated addon-homebridge.