Investigate Echo Glow via Homebridge Alexa Smart Home bridge

## Scope
Track the Amazon Echo Glow path separately from #1122. This is a different implementation from the Echo Dot LED ring / Night Light skill idea: the likely path is exposing Amazon devices back into Home Assistant through a Homebridge bridge, then automating the resulting Home Assistant entity.

Gear reference: Echo Glow - https://amzn.to/4wsGUoU

## Current research
- Echo Glow is controlled through the Alexa app and Alexa routines; Home Assistant's Alexa Smart Home Skill path mainly exposes HA entities to Alexa, not Alexa devices back into HA.
- The Home Assistant Community suggestion is to use Homebridge plus the Homebridge Alexa Smart Home plugin, then let Home Assistant discover those devices through the HomeKit Device integration.
- Candidate flow: Amazon Echo Glow -> Homebridge Alexa Smart Home plugin -> HomeKit bridge -> Home Assistant HomeKit Device integration -> HA automations.

## Implementation notes from the HA Community thread
1. Install Homebridge. The forum example used a Raspberry Pi 3 and the Homebridge Raspberry Pi image.
2. Open the Homebridge UI at `http://YOUR_HOMEBRIDGE_HOST:8581/plugins`.
3. Install `Homebridge Alexa Smart Home` by `@joeyhage`.
4. Follow the plugin setup to add Amazon devices.
5. In Home Assistant, add the `HomeKit Device` integration so HA can discover the Homebridge-exposed Amazon devices.
6. Confirm what entity type Echo Glow exposes as, and whether on/off, brightness, color, and effects are all available.

## Links
- HA Community discussion: https://community.home-assistant.io/t/integration-of-amazon-smart-devices-to-home-assistant-smart-thermostat-echo-glow-smart-plug/956718/3
- Homebridge: https://homebridge.io/
- Homebridge Raspberry Pi image: https://github.com/homebridge/homebridge-raspbian-image
- Homebridge Alexa Smart Home plugin: https://github.com/joeyhage/homebridge-alexa-smarthome
- Home Assistant HomeKit Device integration: https://www.home-assistant.io/integrations/homekit_controller/

## Acceptance criteria
- Echo Glow appears in Home Assistant as a usable entity.
- HA can turn it on/off and, if exposed, set brightness/color for notification use.
- Add one simple automation example, such as setting the Glow red while a door is open/unlocked and clearing it when secure.
- Document any cloud/auth dependency or reliability caveat before wiring this into production notifications.

Start with the Homebridge plugins page at http://YOUR_HOMEBRIDGE_HOST:8581/plugins, the Homebridge Alexa Smart Home plugin, and Home Assistant's HomeKit Device integration. Follow the documented bridge setup, then confirm the Echo Glow entity type and available on/off, brightness, color, and effects controls in Home Assistant. Done means a usable entity, one door-status automation, and documented cloud, authentication, or reliability caveats.

Written by the indexing model from the issue text.