### 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)

Ref<DirAccess> dir_access{ DirAccess::open(p_path, &dir_access_error) ;
	if (dir_access_error != OK) {
		return dir_access_error;
	
	dir_access->list_dir_begin();
	String current_file{ dir_access->get_next() ;
	while (!current_file.is_empty()) {
		String current_file_path{ p_path.path_join(current_file) ;
		if (current_file == ".." || current_file == ".") {
			current_file = dir_access->get_next();
			continue;
		
		if (extensions_to_sign.find(current_file.get_extension()) > -1) {
			Error code_sign_error{ _code_sign(p_preset, current_file_path, p_ent_path, false) ;
			if (code_sign_error != OK) {
				return code_sign_error;
			
			if (is_executable(current_file_path)) {
				// chmod with 0755 if the file is executable.
				FileAccess::set_unix_permissions(current_file_path, 0755);
			
		 else if (dir_access->current_is_dir()) {
			Error code_sign_error{ _code_sign_directory(p_preset, current_file_path, p_ent_path, p_should_error_on_non_code) ;
			if (code_sign_error != OK) {
				return code_sign_error;
			
		 else if (p_should_error_on_non_code) {
			add_message(EXPORT_MESSAGE_WARNING, TTR("Code Signing"), vformat(TTR("Cannot sign file %s."), current_file));
			return Error::FAILED;