### 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)

return find_export_template(template_file_name, err) != "";
}
Ref<EditorExportPreset> EditorExportPlatform::create_preset() {
	Ref<EditorExportPreset> preset;
	preset.instantiate();
	preset->platform = Ref<EditorExportPlatform>(this);
	List<ExportOption> options;
	get_export_options(&options);
	Vector<Ref<EditorExportPlugin>> export_plugins = EditorExport::get_singleton()->get_export_plugins();
	for (int i = 0; i < export_plugins.size(); i++) {
		export_plugins.write[i]->_get_export_options(Ref<EditorExportPlatform>(this), &options);
	}
	for (const ExportOption &E : options) {
		StringName option_name = E.option.name;
		preset->properties[option_name] = E.option;
		preset->values[option_name] = E.default_value;
		preset->update_visibility[option_name] = E.update_visibility;
	}
	return preset;
}
void EditorExportPlatform::_export_find_resources(EditorFileSystemDirectory *p_dir, HashSet<String> &p_paths) {