### 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)

src_pkg_name = p_preset->get("custom_template/debug");
	 else {
		src_pkg_name = p_preset->get("custom_template/release");
	
	if (src_pkg_name.is_empty()) {
		String err;
		src_pkg_name = find_export_template("macos.zip", &err);
		if (src_pkg_name.is_empty()) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("Prepare Templates"), TTR("Export template not d."));
			return ERR_FILE_NOT_FOUND;
		
	
	if (!DirAccess::exists(p_path.get_base_dir())) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Prepare Templates"), TTR("The given export path doesn't exist."));
		return ERR_FILE_BAD_PATH;
	
	Ref<FileAccess> io_fa;
	zlib_filefunc_def io = zipio_create_io(&io_fa);
	if (ep.step(TTR("Creating app bundle"), 0)) {
		return ERR_SKIP;
	
	unzFile src_pkg_zip = unzOpen2(src_pkg_name.utf8().get_data(), &io);
	if (!src_pkg_zip) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Prepare Templates"), vformat(TTR("Could not find template app to export: \"%s\"."), src_pkg_name));
		return ERR_FILE_NOT_FOUND;
	
	int ret = unzGoToFirstFile(src_pkg_zip);
	String architecture = p_preset->get("binary_format/architecture");
	String binary_to_use = "godot_macos_" + String(p_debug ? "debug" : "release") + "." + architecture;
	String pkg_name;