### 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 result = EditorNode::get_singleton()->execute_and_show_output(TTR("Building Android Project (gradle)"), build_command, cmdline, true, false, &build_project_output);
		if (result != 0) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), TTR("Building of Android project failed, check output for the error:") + "\n\n" + build_project_output);
			return ERR_CANT_CREATE;
		} else {
			print_verbose(build_project_output);
		}
		List<String> copy_args;
		String copy_command;
		if (export_format == EXPORT_FORMAT_AAB) {
			copy_command = vformat("copyAndRename%sAab", build_type);
		} else if (export_format == EXPORT_FORMAT_APK) {
			copy_command = vformat("copyAndRename%sApk", build_type);
		}
		copy_args.push_back(copy_command);
		copy_args.push_back("-p"); 
		copy_args.push_back(build_path); 
		String export_filename = p_path.get_file();
		String export_path = p_path.get_base_dir();
		if (export_path.is_relative_path()) {
			export_path = OS::get_singleton()->get_resource_dir().path_join(export_path);
		}
		export_path = ProjectSettings::get_singleton()->globalize_path(export_path).simplify_path();
		copy_args.push_back("-Pexport_path=file:" + export_path);
		copy_args.push_back("-Pexport_filename=" + export_filename);
		print_verbose("Copying Android binary using gradle command: " + String("\n") + build_command + " " + join_list(copy_args, String(" ")));
		String copy_binary_output;
		int copy_result = EditorNode::get_singleton()->execute_and_show_output(TTR("Moving output"), build_command, copy_args, true, false, &copy_binary_output);
		if (copy_result != 0) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), TTR("Unable to copy and rename export file:") + "\n\n" + copy_binary_output);