Allow scheduled automations to continue an existing session

### Feature summary

Let an automation optionally add its prompt to an existing project session instead of creating a separate run session.

### What problem are you trying to solve?

I use automations for recurring work that continues the same plan and workspace.

An automation can reuse its workspace, but in the project-bound automation I tested, successive runs each had a separate conversation. The work, tool history, decisions, and summary can therefore become split across run sessions instead of appearing in the session where I normally coordinate the work.

### Proposed solution

Add a **Run in** choice:

- **New automation run** — current behavior and default
- **Existing project session** — queue the automation prompt as a labeled new turn in a selected session

If the session is busy, the prompt should wait rather than steer the active work. If the target has been deleted, belongs to another project, or cannot be resumed, the run should fail clearly instead of silently creating another session.

The automation run should link to the resulting turn. Interactive, Plan, and Autopilot should be selectable for that turn.

### Workflow impact

Recurring work could stay in one continuous, auditable conversation without changing the current isolated-run behavior for existing automations.

### Installation context

GitHub Copilot app 1.1.1 on Windows x64, OS build 26200.8893, using a local project automation.

### Additional context

Related:

- #173 requests promoting a workflow run to a session.
- #1150 requests project-scoped automation actions in the session UI.

Copilot CLI also supports scheduling prompts in the current session with `/every` and `/after`, but only while that session is running:
https://docs.github.com/en/copilot/how-tos/copilot-cli/automate-copilot-cli/schedule-prompts

This request is for the same-session option to work as a durable GitHub Copilot App automation destination.

No implementation files, tests, or entry points are identified. Start by reading related issues #173 and #1150 and the linked Copilot CLI scheduling documentation, then determine where project automations select and resume sessions. Done means supporting the new destination and its stated busy, deleted, ownership, failure, linking, and interaction-mode behaviors without changing the default isolated-run behavior.

Written by the indexing model from the issue text.