feat: Chrome extension Side Panel + Conductor API proposal

Chrome extension (Manifest V3, sideload):
- Side Panel with live activity feed, @ref overlays, dark terminal aesthetic
- Background worker: health polling, SSE relay, ref fetching
- Popup: port config, connection status, side panel launcher
- Content script: floating ref panel with @ref badges

Conductor API proposal (docs/designs/CONDUCTOR_SESSION_API.md):
- SSE endpoint for full Claude Code session mirroring in Side Panel
- Discovery via HTTP endpoint (not filesystem — extensions can't read files)

TODOS.md: add $B watch, multi-agent tabs, cross-platform CDP, Web Store publishing.
Mark CDP mode as shipped.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

docs/designs/CONDUCTOR_SESSION_API.md

@@ -0,0 +1,108 @@
+# Conductor Session Streaming API Proposal
+
+## Problem
+
+When Claude controls your real browser via CDP (gstack `$B connect`), you look at two
+windows: **Conductor** (to see Claude's thinking) and **Chrome** (to see Claude's actions).
+
+gstack's Chrome extension Side Panel shows browse activity — every command, result,
+and error. But for *full* session mirroring (Claude's thinking, tool calls, code edits),
+the Side Panel needs Conductor to expose the conversation stream.
+
+## What this enables
+
+A "Session" tab in the gstack Chrome extension Side Panel that shows:
+- Claude's thinking/content (truncated for performance)
+- Tool call names + icons (Edit, Bash, Read, etc.)
+- Turn boundaries with cost estimates
+- Real-time updates as the conversation progresses
+
+The user sees everything in one place — Claude's actions in their browser + Claude's
+thinking in the Side Panel — without switching windows.
+
+## Proposed API
+
+### `GET http://127.0.0.1:{PORT}/workspace/{ID}/session/stream`
+
+Server-Sent Events endpoint that re-emits Claude Code's conversation as NDJSON events.
+
+**Event types** (reuse Claude Code's `--output-format stream-json` format):
+
+```
+event: assistant
+data: {"type":"assistant","content":"Let me check that page...","truncated":true}
+
+event: tool_use
+data: {"type":"tool_use","name":"Bash","input":"$B snapshot","truncated_input":true}
+
+event: tool_result
+data: {"type":"tool_result","name":"Bash","output":"[snapshot output...]","truncated_output":true}
+
+event: turn_complete
+data: {"type":"turn_complete","input_tokens":1234,"output_tokens":567,"cost_usd":0.02}
+```
+
+**Content truncation:** Tool inputs/outputs capped at 500 chars in the stream. Full
+data stays in Conductor's UI. The Side Panel is a summary view, not a replacement.
+
+### `GET http://127.0.0.1:{PORT}/api/workspaces`
+
+Discovery endpoint listing active workspaces.
+
+```json
+{
+  "workspaces": [
+    {
+      "id": "abc123",
+      "name": "gstack",
+      "branch": "garrytan/chrome-extension-ctrl",
+      "directory": "/Users/garry/gstack",
+      "pid": 12345,
+      "active": true
+    }
+  ]
+}
+```
+
+The Chrome extension auto-selects a workspace by matching the browse server's git repo
+(from `/health` response) to a workspace's directory or name.
+
+## Security
+
+- **Localhost-only.** Same trust model as Claude Code's own debug output.
+- **No auth required.** If Conductor wants auth, include a Bearer token in the
+  workspace listing that the extension passes on SSE requests.
+- **Content truncation** is a privacy feature — long code outputs, file contents, and
+  sensitive tool results never leave Conductor's full UI.
+
+## What gstack builds (extension side)
+
+Already scaffolded in the Side Panel "Session" tab (currently shows placeholder).
+
+When Conductor's API is available:
+1. Side Panel discovers Conductor via port probe or manual entry
+2. Fetches `/api/workspaces`, matches to browse server's repo
+3. Opens `EventSource` to `/workspace/{id}/session/stream`
+4. Renders: assistant messages, tool names + icons, turn boundaries, cost
+5. Falls back gracefully: "Connect Conductor for full session view"
+
+Estimated effort: ~200 LOC in `sidepanel.js`.
+
+## What Conductor builds (server side)
+
+1. SSE endpoint that re-emits Claude Code's stream-json per workspace
+2. `/api/workspaces` discovery endpoint with active workspace list
+3. Content truncation (500 char cap on tool inputs/outputs)
+
+Estimated effort: ~100-200 LOC if Conductor already captures the Claude Code stream
+internally (which it does for its own UI rendering).
+
+## Design decisions
+
+| Decision | Choice | Rationale |
+|----------|--------|-----------|
+| Transport | SSE (not WebSocket) | Unidirectional, auto-reconnect, simpler |
+| Format | Claude's stream-json | Conductor already parses this; no new schema |
+| Discovery | HTTP endpoint (not file) | Chrome extensions can't read filesystem |
+| Auth | None (localhost) | Same as browse server, CDP port, Claude Code |
+| Truncation | 500 chars | Side Panel is ~300px wide; long content useless |