Add /healthz endpoint

Returns 200 ok if the DB is reachable, 503 if not.

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

main.go

@@ -142,6 +142,15 @@ func main() {
 	r.Use(middleware.Recoverer)
 	r.Use(srv.sessionMiddleware)
 
+	// Health check
+	r.Get("/healthz", func(w http.ResponseWriter, r *http.Request) {
+		if err := database.PingContext(r.Context()); err != nil {
+			http.Error(w, "db down", http.StatusServiceUnavailable)
+			return
+		}
+		w.Write([]byte("ok"))
+	})
+
 	// Static files
 	r.Handle("/static/*", http.FileServer(http.FS(staticFS)))