feat(adminalert): operator email on new feedback / word complaints

New adminalert worker polls for feedback + word complaints arriving since the last check
and coalesces a burst into one digest email per interval (5 min), inert unless a distinct
admin sender (BACKEND_SMTP_ADMIN_FROM) and recipient (BACKEND_ADMIN_EMAIL, comma-separated
allowed) are configured. The mailer gains a per-message From override and splits a
comma-separated To into separate recipients (go-mail needs them as a list). Feedback/game
stores gain CountSince/CountComplaintsSince. Unit tests cover the digest, the skip-when-
empty, and the recipient split.

backend/cmd/backend/main.go

@@ -12,6 +12,7 @@ import (
 	"fmt"
 	"log"
 	"os/signal"
+	"strings"
 	"syscall"
 	"time"
 
@@ -20,6 +21,7 @@ import (
 
 	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/accountmerge"
+	"scrabble/backend/internal/adminalert"
 	"scrabble/backend/internal/ads"
 	"scrabble/backend/internal/banview"
 	"scrabble/backend/internal/config"
@@ -44,6 +46,10 @@ import (
 // telemetryShutdownTimeout bounds the OpenTelemetry flush during process exit.
 const telemetryShutdownTimeout = 5 * time.Second
 
+// adminAlertInterval is how often the operator-alert worker checks for new feedback /
+// complaints; a burst within one interval coalesces into a single digest email.
+const adminAlertInterval = 5 * time.Minute
+
 func main() {
 	cfg, err := config.Load()
 	if err != nil {
@@ -207,6 +213,18 @@ func run(ctx context.Context, cfg config.Config, logger *zap.Logger) error {
 	feedbackSvc := feedback.NewService(feedback.NewStore(db), accounts)
 	feedbackSvc.SetNotifier(hub)
 
+	// Operator alert emails on new feedback / word complaints, coalesced into one digest
+	// per interval. Inert unless a distinct admin sender and recipient are configured.
+	if cfg.SMTP.AdminFrom != "" && cfg.SMTP.AdminTo != "" {
+		consoleURL := ""
+		if cfg.PublicBaseURL != "" {
+			consoleURL = strings.TrimRight(cfg.PublicBaseURL, "/") + "/_gm"
+		}
+		alerts := adminalert.New(mailer, feedbackSvc, games, cfg.SMTP.AdminFrom, cfg.SMTP.AdminTo, consoleURL, logger)
+		go alerts.Run(ctx, adminAlertInterval)
+		logger.Info("admin alert worker started", zap.Duration("interval", adminAlertInterval))
+	}
+
 	// Robot opponent: provision its durable account pool (a hard startup
 	// dependency, like the dictionaries) and start its move driver. The matchmaker
 	// substitutes a pooled robot for a missing human after the wait window.