### Godot version

Godot 4-beta10

### System information

Linux, KDE Neon, OpenGL3, Mesa Intel(R) UHD Graphics (CML GT2)

### Issue description

I can't move to Animation player when I open a AnimatedSprite

See the video:
https://youtu.be/_nyN42rNlTw


### Steps to reproduce

- Open Scene GPlayer
- Select Idle (Animation player) node
- Select Body (Animation sprite) node
- Select animation in bottom tab

### Minimal reproduction project

You can test in my game is open source and don't have many files 👍🏻 

[the-zero-day.zip](https://github.com/godotengine/godot/files/10304677/the-zero-day.zip)

}
			changing++;
			if (update_tree_pending) {
				update_tree_pending = false;
				pending.clear();
				_update_tree();
			} else {
				while (pending.size()) {
					StringName prop = *pending.begin();
					if (editor_property_map.has(prop)) {
						for (EditorProperty *E : editor_property_map[prop]) {
							E->update_property();
							E->update_editor_property_status();
							E->update_cache();
						}
					}
					pending.remove(pending.begin());
				}
			}
			changing--;
		} break;
		case EditorSettings::NOTIFICATION_EDITOR_SETTINGS_CHANGED: {
			_update_inspector_bg();
			if (EditorSettings::get_singleton()->check_changed_settings_in_group("interface/inspector")) {
				update_tree();
			}
		} break;
	}
}
void EditorInspector::_changed_callback() {