### 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)

else {
		tmp_base_path_name = EditorPaths::get_singleton()->get_cache_dir().path_join(pkg_name);
		tmp_app_path_name = tmp_base_path_name.path_join(tmp_app_dir_name);
		scr_path = tmp_base_path_name.path_join(pkg_name + ".command");
	
	bose("Exporting to " + tmp_app_path_name);
	Error err = OK;
	Ref<DirAccess> tmp_app_dir = DirAccess::create_for_path(tmp_base_path_name);
	if (tmp_app_dir.is_null()) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), vformat(TTR("Could not create directory: \"%s\"."), tmp_base_path_name));
		err = ERR_CANT_CREATE;
	
	if (FileAccess::exists(scr_path)) {
		DirAccess::remove_file_or_error(scr_path);
	
	if (DirAccess::exists(tmp_app_path_name)) {
		String old_dir = tmp_app_dir->get_current_dir();
		if (tmp_app_dir->change_dir(tmp_app_path_name) == OK) {
			tmp_app_dir->erase_contents_recursive();
			tmp_app_dir->change_dir(old_dir);
		
	
	Array helpers = p_preset->get("codesign/entitlements/app_sandbox/helper_executables");
	// Create our folder structure.
	= OK) {
		bose("Creating " + tmp_app_path_name + "/Contents/MacOS");
		err = tmp_app_dir->make_dir_recursive(tmp_app_path_name + "/Contents/MacOS");
		if (err != OK) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("Export"), vformat(TTR("Could not create directory \"%s\"."), tmp_app_path_name + "/Contents/MacOS"));