feat: production hardening — slog, rate limiting, integration tests, seed data (Phase 4)

- Structured logging: replace log.* with log/slog JSON output across backend
- Request logger middleware: logs method, path, status, duration for all non-health requests
- Rate limiting: token bucket (5 req/min, burst 10) on AI endpoints (/api/ai/*)
- Integration tests: full critical path test (auth -> create case -> add deadline -> dashboard)
- Seed demo data: 1 tenant, 5 cases with deadlines/appointments/parties/events
- docker-compose.yml: add all required env vars (DATABASE_URL, SUPABASE_*, ANTHROPIC_API_KEY)
- .env.example: document all env vars including DATABASE_URL and CalDAV note

backend/internal/services/caldav_service.go

@@ -4,7 +4,7 @@ import (
 	"context"
 	"encoding/json"
 	"fmt"
-	"log"
+	"log/slog"
 	"strings"
 	"sync"
 	"time"
@@ -83,14 +83,14 @@ func (s *CalDAVService) Start() {
 	s.wg.Go(func() {
 		s.backgroundLoop()
 	})
-	log.Println("CalDAV sync service started")
+	slog.Info("CalDAV sync service started")
 }
 
 // Stop gracefully stops the background sync.
 func (s *CalDAVService) Stop() {
 	close(s.stopCh)
 	s.wg.Wait()
-	log.Println("CalDAV sync service stopped")
+	slog.Info("CalDAV sync service stopped")
 }
 
 // backgroundLoop polls tenants at their configured interval.
@@ -113,7 +113,7 @@ func (s *CalDAVService) backgroundLoop() {
 func (s *CalDAVService) syncAllTenants() {
 	configs, err := s.loadAllTenantConfigs()
 	if err != nil {
-		log.Printf("CalDAV: failed to load tenant configs: %v", err)
+		slog.Error("CalDAV: failed to load tenant configs", "error", err)
 		return
 	}
 
@@ -137,7 +137,7 @@ func (s *CalDAVService) syncAllTenants() {
 			ctx, cancel := context.WithTimeout(context.Background(), 2*time.Minute)
 			defer cancel()
 			if _, err := s.SyncTenant(ctx, tid, c); err != nil {
-				log.Printf("CalDAV: sync failed for tenant %s: %v", tid, err)
+				slog.Error("CalDAV: sync failed", "tenant_id", tid, "error", err)
 			}
 		}(tenantID, cfg)
 	}
@@ -649,7 +649,7 @@ func (s *CalDAVService) logConflictEvent(ctx context.Context, tenantID, caseID u
 		VALUES ($1, $2, $3, 'caldav_conflict', $4, $5, $6, NOW(), NOW())`,
 		uuid.New(), tenantID, caseID, "CalDAV sync conflict", msg, metadata)
 	if err != nil {
-		log.Printf("CalDAV: failed to log conflict event: %v", err)
+		slog.Error("CalDAV: failed to log conflict event", "error", err)
 	}
 }