Track if intent was processed locally

Proposed change

Track if a intent was processed locally, this way we can show it on the assist pipeline debug page

Frontend PR: https://github.com/home-assistant/frontend/pull/23115

Type of change

[ ] Dependency upgrade
[ ] Bugfix (non-breaking change which fixes an issue)
[ ] New integration (thank you!)
[x] New feature (which adds functionality to an existing integration)
[ ] Deprecation (breaking change to happen in the future)
[ ] Breaking change (fix/feature causing existing functionality to break)
[ ] Code quality improvements to existing code or addition of tests

Additional information

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

Checklist

[x] The code change is tested and works locally.
[x] Local tests pass. Your PR cannot be merged unless tests pass
[x] There is no commented out code in this PR.
[x] I have followed the development checklist
[x] I have followed the perfect PR recommendations
[x] The code has been formatted using Ruff (ruff format homeassistant tests)
[x] 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

If the code communicates with devices, web services, or third-party tools:

[ ] The manifest file has all fields filled out correctly.
Updated and included derived files by running: python3 -m script.hassfest.
[ ] New or updated dependencies have been added to requirements_all.txt.
Updated by running python3 -m script.gen_requirements_all.
[ ] For the updated dependencies - a link to the changelog, or at minimum a diff between library versions is added to the PR description.

To help with the load of incoming pull requests:

[x] I have reviewed two other open pull requests in this repository.

Hey there @balloob, @synesthesiam, mind taking a look at this pull request as it has been labeled with an integration (assist_pipeline) you are listed as a code owner for? Thanks!

Code owner commands

Code owners of `assist_pipeline` can trigger bot actions by commenting: - `@home-assistant close` Closes the pull request. - `@home-assistant rename Awesome new title` Renames the pull request. - `@home-assistant reopen` Reopen the pull request. - `@home-assistant unassign assist_pipeline` Removes the current integration label and assignees on the pull request, add the integration domain after the command. - `@home-assistant add-label needs-more-information` Add a label (needs-more-information, problem in dependency, problem in custom component) to the pull request. - `@home-assistant remove-label needs-more-information` Remove a label (needs-more-information, problem in dependency, problem in custom component) on the pull request.

home-assistant / core