feat(search): add PostgreSQL FTS on AI sessions with Command Palette integration

- Migration: add generated tsvector column + GIN index on ai_sessions (problem_summary, resolution_summary, escalation_reason, problem_domain)
- Backend: wire FTS into list_sessions q param; add GET /ai-sessions/search endpoint returning AISessionSearchResult (registered before /{session_id} to avoid UUID routing conflict)
- Frontend: add AISessionSearchResult type, aiSessionsApi.search() method, and Command Palette group "FlowPilot Sessions" using Zap icon navigating to /pilot/:id

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

backend/app/api/endpoints/ai_sessions.py

@@ -16,7 +16,7 @@ from typing import Annotated, Optional
 from uuid import UUID
 
 from fastapi import APIRouter, Depends, HTTPException, Query, Request, status
-from sqlalchemy import or_, select, func
+from sqlalchemy import or_, select, func, text
 from sqlalchemy.ext.asyncio import AsyncSession
 from sqlalchemy.orm import selectinload
 
@@ -41,6 +41,7 @@ from app.schemas.ai_session import (
     AISessionSummary,
     AISessionDetail,
     AISessionStepResponse,
+    AISessionSearchResult,
     StepOptionSchema,
 )
 from app.services import flowpilot_engine
@@ -454,6 +455,44 @@ async def link_ticket_to_session(
     return detail
 
 
+# ── Search sessions (Command Palette) ──
+
+@router.get("/search", response_model=list[AISessionSearchResult])
+@limiter.limit("30/minute")
+async def search_sessions(
+    request: Request,
+    current_user: Annotated[User, Depends(get_current_active_user)],
+    db: Annotated[AsyncSession, Depends(get_db)],
+    q: str = Query(..., min_length=2, max_length=200),
+    limit: int = Query(5, ge=1, le=20),
+):
+    """Search AI sessions by content using full-text search. Used by Command Palette."""
+    result = await db.execute(
+        select(AISession)
+        .where(
+            or_(
+                AISession.user_id == current_user.id,
+                AISession.account_id == current_user.account_id,
+            ),
+            text("ai_sessions.search_vector @@ plainto_tsquery('english', :q)"),
+        )
+        .params(q=q)
+        .order_by(AISession.created_at.desc())
+        .limit(limit)
+    )
+    sessions = result.scalars().all()
+    return [
+        AISessionSearchResult(
+            id=s.id,
+            problem_summary=s.problem_summary,
+            problem_domain=s.problem_domain,
+            status=s.status,
+            created_at=s.created_at,
+        )
+        for s in sessions
+    ]
+
+
 # ── List sessions ──
 
 @router.get("", response_model=list[AISessionSummary])
@@ -502,7 +541,10 @@ async def list_sessions(
         query = query.where(AISession.created_at >= date_from)
     if date_to:
         query = query.where(AISession.created_at <= date_to)
-    # TODO: Full-text search via q param — see Task 7
+    if q:
+        query = query.where(
+            text("ai_sessions.search_vector @@ plainto_tsquery('english', :q)")
+        ).params(q=q)
 
     result = await db.execute(query)
     sessions = result.scalars().all()