Add email sync service for automated job application tracking

Background poller fetches emails via IMAP or Microsoft Graph API,
classifies them with Claude Haiku, and creates/updates JobApplication
records automatically. Includes manual sync endpoint and OAuth callback.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

backend/handlers/handle_email_sync.go

@@ -0,0 +1,45 @@
+package handlers
+
+import (
+	"log"
+	"net/http"
+
+	"github.com/gin-gonic/gin"
+)
+
+func (store *Store) TriggerEmailSync(ctx *gin.Context) {
+	if store.EmailSync == nil || store.EmailSync.HTTPClient == nil {
+		ctx.JSON(http.StatusServiceUnavailable, gin.H{"error": "email sync not configured or not authenticated"})
+		return
+	}
+
+	err := store.EmailSync.SyncEmails(ctx.Request.Context())
+	if err != nil {
+		log.Printf("[EmailSync] Manual sync error: %v", err)
+		ctx.JSON(http.StatusInternalServerError, gin.H{"error": "sync failed", "details": err.Error()})
+		return
+	}
+
+	ctx.JSON(http.StatusOK, gin.H{"message": "sync completed"})
+}
+
+func (store *Store) CompleteEmailAuth(ctx *gin.Context) {
+	if store.EmailSync == nil {
+		ctx.JSON(http.StatusServiceUnavailable, gin.H{"error": "email sync not configured"})
+		return
+	}
+
+	code := ctx.Query("code")
+	if code == "" {
+		ctx.JSON(http.StatusBadRequest, gin.H{"error": "missing authorization code"})
+		return
+	}
+
+	if err := store.EmailSync.CompleteAuth(ctx.Request.Context(), code); err != nil {
+		log.Printf("[EmailSync] Auth completion error: %v", err)
+		ctx.JSON(http.StatusInternalServerError, gin.H{"error": "authentication failed"})
+		return
+	}
+
+	ctx.JSON(http.StatusOK, gin.H{"message": "email authentication successful"})
+}