Feature Request: Plan status indicators (badge/symbol) on session list items

### Describe the feature or problem you'd like to solve

When managing multiple sessions, there's no visual way to tell at a glance what stage each session's plan is in. You have to open each session to check progress, which breaks flow when juggling several workstreams.

### Proposed solution

Add a small status indicator (symbol with tooltip, or badge) on each session item in the sidebar that reflects the current plan state:

| Status | Meaning | Suggested Icon |
|--------|---------|----------------|
| **Planning** | Agent is actively generating/refining the plan | 🔄 or spinner |
| **PlanReady** | Plan has been generated and is awaiting user approval or kickoff | 📋 or checkmark-outline |
| **PlanInProgress** | Plan has been approved and work is underway | ⚙️ or progress indicator |
| **PlanComplete** | All plan steps are done | ✅ or filled checkmark |

**Requirements:**
- The indicator should be compact enough to not clutter the session list
- A tooltip on hover should show the full status label (e.g., "Plan In Progress")
- Status should update in real-time as the session progresses
- Sessions without a plan (e.g., chat sessions, sessions in interactive/autopilot mode) can omit the indicator or show a neutral state

### Example prompts or workflows

1. User has 5 project sessions open
2. Glancing at the sidebar, they can immediately see:
- Session A: ✅ (done, ready to review/merge)
- Session B: ⚙️ (agent is executing the plan)
- Session C: 📋 (plan ready, waiting for approval)
- Session D: 🔄 (still planning)
3. User clicks Session C to approve the plan, then moves on — no wasted context-switching

### Additional context

Related to #981 (Status Sidebar). This is a lighter-weight version focused specifically on plan lifecycle visibility in the existing session list UI.

Start by locating the existing session list/sidebar and the plan lifecycle state used by sessions. Trace how planning, approval, execution, and completion updates are propagated, then verify that compact indicators, hover labels, real-time updates, and plan-less sessions match the stated requirements.

Written by the indexing model from the issue text.