[FEATURE] Add terminal_title to hook JSON payload for session identification

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Problem Statement

When running multiple Claude Code sessions, notification hooks cannot identify
which terminal/session triggered the notification. Claude Code sets the terminal
tab title (e.g., "Codebase Understanding"), but this information is not included
in hook payloads.

Current hook payload:

{
  "session_id": "abc123",
  "cwd": "C:\\Projects\\my-project",
  "transcript_path": "...",
  "hook_event_name": "Notification",
  "notification_type": "permission_prompt",
  "message": "Claude needs your permission to use Bash"
}

Proposed Solution

Requested addition:

{
  "session_id": "abc123",
  "cwd": "C:\\Projects\\my-project",
  "terminal_title": "Codebase Understanding",  // <-- ADD THIS
  "transcript_path": "...",
  "hook_event_name": "Notification",
  "notification_type": "permission_prompt",
  "message": "Claude needs your permission to use Bash"
}

Use Case

Custom notification scripts need to show which Claude Code session needs attention.
The folder name (from cwd) is often not descriptive enough when working on
multiple tasks in the same project.

Since Claude Code already sets the terminal title internally, this should be
straightforward to include in the hook payload.

Related Issues

• #2112 - Custom session names (related but different)
• #7881 - Subagent identification (similar problem)

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_