### 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)

export_project->set_file_mode(EditorFileDialog::FILE_MODE_SAVE_FILE);
	export_project->popup_file_dialog();
}
void ProjectExportDialog::_export_project_to_path(const String &p_path) {
	
	default_filename = p_path.get_file().get_basename();
	EditorSettings::get_singleton()->set_project_metadata("export_options", "default_filename", default_filename);
	Ref<EditorExportPreset> current = get_current_preset();
	ERR_FAIL_COND_MSG(current.is_null(), "Failed to start the export: current preset is invalid.");
	Ref<EditorExportPlatform> platform = current->get_platform();
	ERR_FAIL_COND_MSG(platform.is_null(), "Failed to start the export: current preset has no valid platform.");
	current->set_export_path(p_path);
	exporting = true;
	platform->clear_messages();
	Error err = platform->export_project(current, export_debug->is_pressed(), current->get_export_path(), 0);
	result_dialog_log->clear();
	if (err != ERR_SKIP) {
		if (platform->fill_log_messages(result_dialog_log, err)) {
			result_dialog->popup_centered_ratio(0.5);
		}
	}
	exporting = false;
}
void ProjectExportDialog::_export_all_dialog() {
#ifndef ANDROID_ENABLED
	export_all_dialog->show();
	export_all_dialog->popup_centered(Size2(300, 80));
#endif
}
void ProjectExportDialog::_export_all_dialog_action(const String &p_str) {