Expose status of Assist as a sensor

**Is your feature request related to a problem? Please describe.**

When I listen to speech(audiobook, podcast, news,etc.) on my home sound system, assist can not distinguish between my voice and surrounding sound, and never stops listening.

**Describe the solution you'd like**

I would like to mute my home sound system, when assist is listening (like I do with Voice PE).
To do this we need a sensor in the companion-app, that shows, whether assist on the phone is listening.

We could have different state
- CLOSED: Assist is not opened
- SPEAKING: Assist is speaking
- LISTENING: Assist is listening
- IDLE: Assist is opened but not doing anything

This feature request comes from https://community.home-assistant.io/t/sensor-for-assist-listening-on-phone/907054

Review the linked pull request #6098 first, then compare it with the requested CLOSED, SPEAKING, LISTENING, and IDLE states. Done means the Android companion app exposes Assist's current listening status as a sensor with the requested state behavior.

Written by the indexing model from the issue text.