### 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)

bool convert_text_to_binary = GLOBAL_GET("editor/export/convert_text_resources_to_binary");
	if (convert_text_to_binary || !customize_resources_plugins.is_empty() || !customize_scenes_plugins.is_empty()) {
		
		Ref<FileAccess> f = FileAccess::open(export_base_path.path_join("file_cache"), FileAccess::READ);
		if (f.is_valid()) {
			String l = f->get_line();
			while (l != String()) {
				Vector<String> fields = l.split("::");
				if (fields.size() == 4) {
					FileExportCache fec;
					String path = fields[0];
					fec.source_md5 = fields[1].strip_edges();
					fec.source_modified_time = fields[2].strip_edges().to_int();
					fec.saved_path = fields[3];
					fec.used = false; 
					export_cache[path] = fec;
				}
				l = f->get_line();
			}
		} else {
			
			Ref<DirAccess> d = DirAccess::create(DirAccess::ACCESS_RESOURCES);
			d->change_dir(ProjectSettings::get_singleton()->get_project_data_path());
			d->make_dir_recursive("exported/" + itos(custom_resources_hash));
		}
	}
	
	int idx = 0;
	int total = paths.size();
	for (const String &E : paths) {