### 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)

Vector<PluginConfigAndroid> enabled_plugins;
	Vector<PluginConfigAndroid> all_plugins = get_plugins();
	for (int i = 0; i < all_plugins.size(); i++) {
		PluginConfigAndroid plugin = all_plugins[i];
		bool enabled = p_presets->get("plugins/" + plugin.name);
		if (enabled) {
			enabled_plugins.push_back(plugin);
		}
	}
	return enabled_plugins;
}
#endif 
Error EditorExportPlatformAndroid::store_in_apk(APKExportData *ed, const String &p_path, const Vector<uint8_t> &p_data, int compression_method) {
	zip_fileinfo zipfi = get_zip_fileinfo();
	zipOpenNewFileInZip(ed->apk,
			p_path.utf8().get_data(),
			&zipfi,
			nullptr,
			0,
			nullptr,
			0,
			nullptr,
			compression_method,
			Z_DEFAULT_COMPRESSION);
	zipWriteInFileInZip(ed->apk, p_data.ptr(), p_data.size());
	zipCloseFileInZip(ed->apk);
	return OK;
}
Error EditorExportPlatformAndroid::save_apk_so(void *p_userdata, const SharedObject &p_so) {