[FEATURE] Display conversation topic summary in status bar

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

Power users running multiple Claude Code sessions across terminal tabs have no way to identify which session is which without scrolling up through the conversation. The bottom status bar (which displays "accept edits on ..." and similar persistent text) has unused horizontal space to the right, but there's no mechanism to display session-identifying context there.

Proposed Solution

Auto-generate a short conversation topic label (3-5 words, or whatever fits the remaining horizontal space) and display it right-justified in the bottom status bar. The label would be derived from the conversation context by the LLM and updated as the topic shifts. Since the model already has the full conversation context, generating a brief summary is trivial and adds no meaningful latency or cost.

Example rendering:

accept edits on src/components/auth.tsx fixing OAuth token refresh

Alternative Solutions

1. /rename command — Users can manually name sessions, but names are only visible in the /resume picker, not in the active terminal tab. Requires manual effort and doesn't update as topics shift.

1. Status line configuration — The existing status line feature runs shell commands and can display project/directory info, but shell commands can't access conversation context, so they can't generate topic summaries.

1. Manual terminal title — Users can set terminal tab titles via escape codes (echo -ne "\033]0;topic\007"), but this is manual, doesn't auto-update, and requires breaking out of the Claude Code session.

1. CLAUDE.md instruction — Users could instruct Claude to set the terminal title as part of each response, but this is fragile, adds noise to every interaction, and uses a shell escape code hack rather than a proper UI integration.

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

A DE manager has 4 terminal tabs open:
Tab 1: Debugging a capacity quota issue
Tab 2: Drafting an update about team accomplishments
Tab 3: Profiling writing style from chat history
Tab 4: Reviewing code change for a direct report

Today, all 4 tabs look identical. The user cycles through tabs, reads partial output, and tries to remember which is which. With this feature, each tab's status bar would show a right-justified label like "capacity quota debug", "drafting team update", "chat writing style profile", "reviewing pipeline change".

Additional Context

• The bottom status bar already exists and has unused horizontal space in most terminal widths
• The LLM already has the conversation context needed to generate the label — no additional API calls or retrieval needed
• Label length could be dynamically calculated based on available space (terminal width minus existing status bar content)
• Could be gated behind a setting (e.g., "showConversationTopic": true) for users who prefer a minimal UI
• Natural update cadence: regenerate the label when the topic meaningfully shifts, not on every message