Add Support for Update Entities in Home Assistant for Docker ESPHome Installations

**Describe the problem you have/What new integration you would like**

When using the ESPHome integration with Home Assistant in a Docker setup, the “update” entity is missing. This makes it difficult to manage and perform updates for ESPHome devices from within Home Assistant. I would like to request the addition of support for update entities in the ESPHome integration for Docker installations, similar to how the integration works with the ESPHome add-on.

**Please describe your use case for this integration and alternatives you've tried:**

In my current Docker-based Home Assistant + ESPHome setup, I have successfully integrated ESPHome devices but lack the capability to push updates to these devices directly from Home Assistant. I have verified that the integration is correctly configured and that the ESPHome devices are visible in Home Assistant.

**Additional context**

The absence of update entities in Docker-based setups limits the ease of managing ESPHome devices compared to Home Assistant’s add-on-based installations. Adding support for update entities would streamline the update process and provide a more consistent experience across different Home Assistant installation methods. This feature would greatly enhance usability for users running Home Assistant in Docker environments and improve overall device management.

Start by comparing the Docker-based ESPHome integration with the ESPHome add-on behavior described in the request. Confirm how update entities should appear for integrated ESPHome devices and verify that Docker installations can push device updates from Home Assistant; done means the entities are available and the update flow works consistently.

Written by the indexing model from the issue text.