webclient: background task chip, id-first tool matching, queued badge ...

- toolIndex (tool_call_id → card): exact matching for parallel batches and
  late events after stream_end; legacy name+pending fallback kept
- bare tool_call synthesizes a card so results are never lost
- task_update: backgroundTasks chip above composer + steps appended to the
  spawning tool card (parent_tool_call_id binding)
- message_queued badge, terminal_opened dispatch
- new BackgroundTasksChip component, task_update step rendering in ToolCard

Add session search across messages with backend + frontend ...

Backend:
- GET /sessions now accepts `search` query param
- _session_summary computes match_indices and match_preview from messages
- pg_session_store: messages ILIKE added to search_list and count_all
- In-memory store: search_list also filters by message content

Frontend:
- AppSidebar: search toggle icon + debounced input, Ctrl+K shortcut
- SessionItem: highlight matching text, show match_preview from search
- SessionList: pass searchQuery to SessionItem
- SessionsStore: searchQuery/searchActive state, setSearch/clearSearch
- API layer: getSessions accepts search param
- MessageList: scroll to target message + brightness flash animation
- ChatStore: loadSession accepts targetMessageIndex, scrollToMessageIndex ref
- CSS: msg-flash keyframe animation in app.scss
- Tests updated for new getSessions signature

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

Paginate session list loading

Refine 3D modeler workflow

Add webclient unit tests (Vitest) — 47 tests ...

- Vitest + @vue/test-utils + happy-dom setup
- api/index.test.js: 8 tests for fetch wrapper, verbs, errors, FormData
- stores/chat.test.js: 23 tests for buildMessageList, WS handlers, load/clear
- stores/sessions.test.js: 6 tests for fetch, create, delete, pin, preview
- stores/profiles.test.js: 3 tests for fetch, auto-select, lookup
- composables/useWebSocket.test.js: 7 tests with MockWebSocket
- Export buildMessageList from chat store so tests can verify message parsing
- Update docs/testing.md with webclient stack, layout, and commands

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>