Add tasks serve CLI and local server with heartbeat or task-manager status UI

Problem

MkDocs is strong for static narrative docs but weak for live task-queue and heartbeat visibility. Operators need a small local server that browses plan markdown and shows task-manager snapshot / register (and later escalation flags) without opening raw JSON.

Context

• Entry today: just plan … → tasks/tools/plans_cli.py; docs: just plan serve (MkDocs).
• Snapshot path pattern: tasks/logs/task_manager/task-manager-<owner>.snapshot.json (gitignored); register alongside.
• Naming goal: converge on tasks as the user-facing umbrella (tasks serve); repo path may stay tasks/ until rename-master-plans-tree-to-tasks.
• Already landed prerequisites on main:
• PR #711: structured escalation payload (escalation.required, escalation.signals[]) and default no-mutate dispatch behavior for started_at.
• PR #705: PR-CI task signals and default task worktree root under .worktrees/<slug>.
• Server /status page should consume both escalation and PR-CI fields from the snapshot without assuming legacy sibling worktree paths.

Possible Solutions

• A — Flask/FastAPI + markdown render: Single process, Jinja or htmx, read files from disk; poll snapshot mtime or SSE later.
• B — Extend existing playground patterns: Reuse repo conventions if a tiny app already fits.
• Recommended: A minimal FastAPI or Starlette app colocated under tasks/tools/ or tasks/ package, invoked via plans tasks serve or uv run … until rename.

Plan

• [x] Add CLI subcommand (e.g. plans tasks serve --port …) that starts the server; document in tasks/tools/cli-reference.md.
• [x] Implement markdown browsing (safe path under repo root) and a /status (or /dashboard) page reading latest snapshot + register for TASK_MANAGER_OWNER or --owner.
• [x] Phase 1: keep MkDocs as parallel option; README/AGENTS note “MkDocs vs tasks serve”.
• [x] Tests: lightweight handler tests or subprocess smoke for CLI entrypoint.

Implementation Progress

• Added tasks/tools/tasks_server.py:
• FastAPI app with /healthz, /status, /status.json
• /status reads owner-scoped snapshot/register from tasks/logs/task_manager
• markdown browser under repo root: /browse + /browse/{path}
• path safety guard prevents traversal outside repository root
• Added plans serve CLI entry in tasks/tools/plans_cli.py:
• --host (default 127.0.0.1)
• --port (default 8005)
• --owner (default TASK_MANAGER_OWNER then current system user)
• uses uvicorn to run the task server app
• Updated tasks/tools/cli-reference.md with server command docs and explicit parallel usage note:
• plans serve for live status tooling
• just plans for MkDocs static docs
• Added tests:
• tests/core/test_tasks_server.py for status + browse endpoints
• tests/core/test_plans_cli.py parser/delegation tests for serve
• Validation run:
• uv run pytest tests/core/test_plans_cli.py tests/core/test_tasks_server.py -q (47 passed)

QA Exploration

• N/A (internal local tooling server page, validated via endpoint/unit tests)
• [x] QA exploration completed (or N/A for non-UI tasks)

Review Feedback

• [ ] Review cleared