Full pipeline flow through web interface with live updates

API:
  POST /api/tasks/{id}/run — sets task to in_progress immediately,
    launches subprocess with error handling and logging.
  GET /api/tasks/{id}/running — checks pipelines table for active run.
  Fixed --db flag position in subprocess command.

TaskDetail (live pipeline):
  - Run button starts pipeline, auto-starts 3s polling
  - Pipeline cards update in real-time as agent_logs appear
  - Pulsing blue dot on header while in_progress
  - Spinner on run button during execution
  - Auto-stops polling when status changes from in_progress
  - Cleanup on component unmount (no leaked timers)

ProjectView (run from list):
  - [>] button on each pending task row
  - Confirm dialog before starting
  - Pulsing blue dot for in_progress tasks
  - Click task row → /task/:id with live view

Dashboard (live statuses):
  - Pulsing blue dot next to active task count
  - Auto-poll every 5s when any project has active tasks
  - Stops polling when no active tasks

5 new API tests (running endpoint, run sets status, not found).
141 tests total, all passing. Frontend builds clean.

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

tests/test_api.py

@@ -135,6 +135,44 @@ def test_task_pipeline_not_found(client):
     assert r.status_code == 404
 
 
+def test_running_endpoint_no_pipeline(client):
+    r = client.get("/api/tasks/P1-001/running")
+    assert r.status_code == 200
+    assert r.json()["running"] is False
+
+
+def test_running_endpoint_with_pipeline(client):
+    from core.db import init_db
+    from core import models
+    conn = init_db(api_module.DB_PATH)
+    models.create_pipeline(conn, "P1-001", "p1", "debug",
+                           [{"role": "debugger"}])
+    conn.close()
+
+    r = client.get("/api/tasks/P1-001/running")
+    assert r.status_code == 200
+    assert r.json()["running"] is True
+
+
+def test_running_endpoint_not_found(client):
+    r = client.get("/api/tasks/NOPE/running")
+    assert r.status_code == 404
+
+
+def test_run_sets_in_progress(client):
+    """POST /run should set task to in_progress immediately."""
+    r = client.post("/api/tasks/P1-001/run")
+    assert r.status_code == 202
+
+    r = client.get("/api/tasks/P1-001")
+    assert r.json()["status"] == "in_progress"
+
+
+def test_run_not_found(client):
+    r = client.post("/api/tasks/NOPE/run")
+    assert r.status_code == 404
+
+
 def test_project_summary_includes_review(client):
     from core.db import init_db
     from core import models