Add analytics MCP app (embedded dashboard) + tasks_analytics MCP tool

[legreffier]

Summary

Add an analytics MCP app — an embedded MCP Apps surface that renders the
agent-work-analytics dashboard inside an MCP host (e.g. a chat client), reusing
the shared <AnalyticsBoard> React component shipped in #1551.

This is the deferred MCP-app follow-up to #1373 / #1551. #1551 delivered the
reusable analytics UI (@moltnet/task-ui) and the Console integration; the design
explicitly scoped the MCP app as a follow-up built on the exported AnalyticsBoard.

Background

• Add task attempt activity stats for agent work analytics #1373 / feat(tasks): add task activity analytics #1550 added the analytics data: the materialized
  task_attempt_activity_stats table, @moltnet/task-analytics-service, and the
  REST endpoint GET /tasks/analytics/activity returning
  TaskActivityAnalyticsResponse.
• feat: agent work analytics — shared UI surface (#1373) #1551 added the shared UI: @moltnet/task-ui now exports AnalyticsBoard
  (+ TaskActivityAnalyticsResponse, AnalyticsFilters, states) as pure-props
  React components, plus the Console /tasks/analytics page wired to the live
  endpoint (verified by an e2e).

The one surface still missing is the MCP app, so an agent/human interacting
through an MCP host can pull up the same analytics without the Console.

Key constraint: MCP apps use tools, not REST

MCP apps never receive a bearer token or call REST directly — the iframe reads
data through the host bridge via app.callServerTool({ name, arguments })
against deterministic MCP server tools (see apps/mcp-server/src/task-app.ts:
"The iframe never receives a bearer token or talks to REST directly").

#1550 added only the REST endpoint — there is no analytics MCP tool yet. So
this issue has two cohesive parts (the app is inert without the tool → one PR).

Scope

1. MCP server tool tasks_analytics_activity

• New deterministic tool in apps/mcp-server wrapping
  @moltnet/task-analytics-service.getActivityAnalytics.
• TypeBox input schema mirroring the REST query: completedAfter, completedBefore,
  tags, taskTypes, profileIds, diaryIds, claimedByAgentIds, groupBy
  (none|day|tag|taskType|profile|diary|agent|providerModel).
• Team scope resolved from the MCP session (not an x-moltnet-team-id header).
• Returns TaskActivityAnalyticsResponse (same shape as the REST endpoint /
  the generated client / @moltnet/task-ui's type).
• Register in the legreffier MCP tool surface; add to the tool-schema tests.

2. Analytics MCP app libs/analytics-mcp-app (React)

Mirrors libs/entry-explore-mcp-app (the existing React MCP-app precedent —
task-mcp-app is vanilla DOM and can't render the React AnalyticsBoard):

• metadata.ts — ANALYTICS_MCP_APP_NAME = 'moltnet_task_analytics', _TITLE,
  _RESOURCE_URI = 'ui://moltnet/tasks/analytics.html'.
• main.tsx — createRoot → <AnalyticsApp/>.
• AnalyticsApp.tsx — useApp from @modelcontextprotocol/ext-apps/react; seed
  filters from the ontoolinput opener payload; call tasks_analytics_activity
  via a typed callTool; map the tool JSON result → TaskActivityAnalyticsResponse;
  render <AnalyticsBoard> (from @moltnet/task-ui) under MoltThemeProvider.
  Owns the explicit loading/error/empty/ready status mapping (same logic as the
  Console TaskAnalyticsPage).
• adapter/ — tool-caller.ts + tool-calls.ts (typed callTool for
  tasks_analytics_activity, snake_case args mirroring the server schema) +
  mcp-adapter.ts (camelCase filters → snake_case args; result JSON → response
  type). Unit tests mirroring entry-explore-mcp-app/src/adapter/*.test.ts.
• theme-tokens.ts, styles.css, index.ts (re-exports metadata constants),
  singlefile vite.config.ts, tsconfigs, package.json
  (react/react-dom + @modelcontextprotocol/ext-apps + @moltnet/task-ui +
  @themoltnet/design-system).
• Registration: apps/mcp-server/src/analytics-app.ts (mirror task-app.ts /
  entry-explore-app.ts) serving the built HTML resource, plus
  apps/mcp-server/__tests__/analytics-app.test.ts.

Reuse / non-goals

• Reuse: the entire @moltnet/task-ui analytics surface (AnalyticsBoard,
  types, states) is used as-is — no UI re-implementation. Filter shape + status
  mapping are lifted from the Console page.
• Type parity: the app's response type IS @moltnet/task-ui's
  TaskActivityAnalyticsResponse; the MCP tool's TypeBox output maps to it 1:1
  (same mirror-and-assert discipline used in feat: agent work analytics — shared UI surface (#1373) #1551).
• Non-goals: no new metrics/DB work (that's Add task attempt activity stats for agent work analytics #1373/feat(tasks): add task activity analytics #1550); no currency/cost
  (that's Add task and team budget controls for token, turn, and estimated cost usage #1412); no vanilla-DOM re-implementation of the dashboard.

Acceptance criteria

• tasks_analytics_activity MCP tool returns a valid TaskActivityAnalyticsResponse
  for the caller's team, honouring all filters + groupBy.
• libs/analytics-mcp-app renders <AnalyticsBoard> with real data pulled
  through the host bridge, across loading/error/empty/ready states.
• Registered + served by mcp-server; opener tool seeds initial filters.
• Adapter + tool unit tests; mcp-server registration test.
• lint, typecheck, test, build green for the new lib + mcp-server.

References

• Parent: Add task attempt activity stats for agent work analytics #1373 (closed) · UI PR: feat: agent work analytics — shared UI surface (#1373) #1551 · API PR: feat(tasks): add task activity analytics #1550 · cost follow-up: Add task and team budget controls for token, turn, and estimated cost usage #1412
• Template: libs/entry-explore-mcp-app (React MCP app)
• Data: @moltnet/task-analytics-service, libs/task-ui/src/analytics