### 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)

HashSet<String> features = p_platform.get_features(p_preset, p_debug);
	Vector<Ref<EditorExportPlugin>> export_plugins = EditorExport::get_singleton()->get_export_plugins();
	
	for (int i = 0; i < export_plugins.size(); i++) {
		export_plugins.write[i]->set_export_preset(p_preset);
		if (GDVIRTUAL_IS_OVERRIDDEN_PTR(export_plugins[i], _export_begin)) {
			PackedStringArray features_psa;
			for (const String &feature : features) {
				features_psa.push_back(feature);
			}
			export_plugins.write[i]->_export_begin_script(features_psa, p_debug, p_path, p_flags);
		} else {
			export_plugins.write[i]->_export_begin(features, p_debug, p_path, p_flags);
		}
	}
}
EditorExportPlatform::ExportNotifier::~ExportNotifier() {
	Vector<Ref<EditorExportPlugin>> export_plugins = EditorExport::get_singleton()->get_export_plugins();
	for (int i = 0; i < export_plugins.size(); i++) {
		if (GDVIRTUAL_IS_OVERRIDDEN_PTR(export_plugins[i], _export_end)) {
			export_plugins.write[i]->_export_end_script();
		}
		export_plugins.write[i]->_export_end();
		export_plugins.write[i]->set_export_preset(Ref<EditorExportPlugin>());
	}
}
bool EditorExportPlatform::_export_customize_dictionary(Dictionary &dict, LocalVector<Ref<EditorExportPlugin>> &customize_resources_plugins) {