### 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.
int scene_idx = (current_menu_option == FILE_SAVE_SCENE || current_menu_option == FILE_SAVE_AS_SCENE) ? -1 : tab_closing_idx;
			if (file->get_file_mode() == EditorFileDialog::FILE_MODE_SAVE_FILE) {
				bool same_open_scene = false;
				for (int i = 0; i < editor_data.get_edited_scene_count(); i++) {
					if (editor_data.get_scene_path(i) == p_file && i != scene_idx) {
						same_open_scene = true;
					}
				}
				if (same_open_scene) {
					show_warning(TTR("Can't overwrite scene that is still open!"));
					return;
				}
				save_default_environment();
				_save_scene_with_preview(p_file, scene_idx);
				_add_to_recent_scenes(p_file);
				save_editor_layout_delayed();
				if (scene_idx != -1) {
					_discard_changes();
				}
			}
		} break;
		case FILE_SAVE_AND_RUN: {
			if (file->get_file_mode() == EditorFileDialog::FILE_MODE_SAVE_FILE) {
				save_default_environment();
				_save_scene_with_preview(p_file);
				project_run_bar->play_custom_scene(p_file);
			}
		} break;
		case FILE_SAVE_AND_RUN_MAIN_SCENE: {
			ProjectSettings::get_singleton()->set("application/run/main_scene", p_file);