### 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)

for (int i = 0; i < p_dir->get_subdir_count(); i++) {
		_export_find_resources(p_dir->get_subdir(i), p_paths);
	}
	for (int i = 0; i < p_dir->get_file_count(); i++) {
		if (p_dir->get_file_type(i) == "TextFile") {
			continue;
		}
		p_paths.insert(p_dir->get_file_path(i));
	}
}
void EditorExportPlatform::_export_find_customized_resources(const Ref<EditorExportPreset> &p_preset, EditorFileSystemDirectory *p_dir, EditorExportPreset::FileExportMode p_mode, HashSet<String> &p_paths) {
	for (int i = 0; i < p_dir->get_subdir_count(); i++) {
		EditorFileSystemDirectory *subdir = p_dir->get_subdir(i);
		_export_find_customized_resources(p_preset, subdir, p_preset->get_file_export_mode(subdir->get_path(), p_mode), p_paths);
	}
	for (int i = 0; i < p_dir->get_file_count(); i++) {
		if (p_dir->get_file_type(i) == "TextFile") {
			continue;
		}
		String path = p_dir->get_file_path(i);
		EditorExportPreset::FileExportMode file_mode = p_preset->get_file_export_mode(path, p_mode);
		if (file_mode != EditorExportPreset::MODE_FILE_REMOVE) {
			p_paths.insert(path);
		}
	}
}
void EditorExportPlatform::_export_find_dependencies(const String &p_path, HashSet<String> &p_paths) {