### 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)

res = new_res;
							}
							break;
						}
					}
					
					if (res.is_valid() && !res->get_path().is_resource_file() && _export_customize_object(res.ptr(), customize_resources_plugins), true) {
						changed = true;
					}
				}
			} break;
			case Variant::DICTIONARY: {
				Dictionary d = v;
				if (_export_customize_dictionary(d, customize_resources_plugins)) {
					changed = true;
				}
			} break;
			case Variant::ARRAY: {
				Array a = v;
				if (_export_customize_array(a, customize_resources_plugins)) {
					changed = true;
				}
			} break;
			default: {
			}
		}
	}
	return changed;
}
bool EditorExportPlatform::_export_customize_object(Object *p_object, LocalVector<Ref<EditorExportPlugin>> &customize_resources_plugins) {