### Godot version

4.1.dev (dc625bcbfc5b587ba8867481ee7a1f6a567c25d0)

### System information

Mageia 9, Linux

### Issue description

When importing a project in current `master`, the following error is raised for each asset that gets imported:
```
Attempting to parent and popup a dialog that already has a parent.
```

It seems to be raised once per asset, caused by the progress dialog.

CC @bruvzg

### Steps to reproduce

- Import a new project in Godot that contains importable assets, e.g. https://github.com/RPicster/godot4-demo-desert-light

### Minimal reproduction project

See above.
ProjectSettings::get_singleton()->save();
			if (file->get_file_mode() == EditorFileDialog::FILE_MODE_SAVE_FILE) {
				save_default_environment();
				_save_scene_with_preview(p_file);
				project_run_bar->play_main_scene((bool)pick_main_scene->get_meta("from_native", false));
			}
		} break;
		case FILE_EXPORT_MESH_LIBRARY: {
			Ref<MeshLibrary> ml;
			if (file_export_lib_merge->is_pressed() && FileAccess::exists(p_file)) {
				ml = ResourceLoader::load(p_file, "MeshLibrary");
				if (ml.is_null()) {
					show_accept(TTR("Can't load MeshLibrary for merging!"), TTR("OK"));
					return;
				}
			}
			if (ml.is_null()) {
				ml = Ref<MeshLibrary>(memnew(MeshLibrary));
			}
			MeshLibraryEditor::update_library_file(editor_data.get_edited_scene_root(), ml, true, file_export_lib_apply_xforms->is_pressed());
			Error err = ResourceSaver::save(ml, p_file);
			if (err) {
				show_accept(TTR("Error saving MeshLibrary!"), TTR("OK"));
				return;
			}
		} break;
		case RESOURCE_SAVE:
		case RESOURCE_SAVE_AS: {
			ERR_FAIL_COND(saving_resource.is_null());
			save_resource_in_path(saving_resource, p_file);