### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

int export_format = int(p_preset->get("gradle_build/export_format"));
	String export_label = export_format == EXPORT_FORMAT_AAB ? "AAB" : "APK";
	String release_keystore = p_preset->get_or_env("keystore/release", ENV_ANDROID_KEYSTORE_RELEASE_PATH);
	String release_username = p_preset->get_or_env("keystore/release_user", ENV_ANDROID_KEYSTORE_RELEASE_USER);
	String release_password = p_preset->get_or_env("keystore/release_password", ENV_ANDROID_KEYSTORE_RELEASE_PASS);
	String target_sdk_version = p_preset->get("gradle_build/target_sdk");
	if (!target_sdk_version.is_valid_int()) {
		target_sdk_version = itos(DEFAULT_TARGET_SDK_VERSION);
	}
	String apksigner = get_apksigner_path(target_sdk_version.to_int(), true);
	print_verbose("Starting signing of the " + export_label + " binary using " + apksigner);
	if (apksigner == "<FAILED>") {
		add_message(EXPORT_MESSAGE_WARNING, TTR("Code Signing"), vformat(TTR("All 'apksigner' tools located in Android SDK 'build-tools' directory failed to execute. Please check that you have the correct version installed for your target sdk version. The resulting %s is unsigned."), export_label));
		return OK;
	}
	if (!FileAccess::exists(apksigner)) {