Break out assist-chat from voice command dialog

[balloob]

Breaking change

Proposed change

PR to break out the "chat" part of the voice command dialog. That will allow future reuse.

Marked as draft because I couldn't get the styling working 😭

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New feature (thank you!)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests

Example configuration

Additional information

• This PR fixes or closes issue: fixes #
• This PR is related to issue or discussion:
• Link to documentation pull request:

Checklist

• The code change is tested and works locally.
• There is no commented out code in this PR.
• Tests have been added to verify that the new code works.

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated for www.home-assistant.io

[bramkragten]

Do we have a usecase for this?