@@ -156,16 +156,26 @@ export function HostedBrowserWebview(props: {
         }
       }, recovery.delayMs);
     };
+    // A click inside the guest only reaches this document as a webview focus
+    // event, so open menus and popovers never see the outside press that
+    // would dismiss them. Replay it as a pointerdown on the webview itself.
+    const dismissHostPopups = () => {
+      webview.dispatchEvent(
+        new PointerEvent("pointerdown", { bubbles: true, pointerType: "mouse" }),
+      );
+    };
     webview.addEventListener("did-attach", register);
     webview.addEventListener("dom-ready", register);
     webview.addEventListener("render-process-gone", recoverGuest);
+    webview.addEventListener("focus", dismissHostPopups);
     register();
     return () => {
       disposed = true;
       if (recoveryTimeout !== null) clearTimeout(recoveryTimeout);
       webview.removeEventListener("did-attach", register);
       webview.removeEventListener("dom-ready", register);
       webview.removeEventListener("render-process-gone", recoverGuest);
+      webview.removeEventListener("focus", dismissHostPopups);
     };
   }, [clientSettingsHydrated, config, initialSrc, runtimeTabId, webviewGeneration]);