### 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)

case NOTIFICATION_EXIT_TREE: {
			if (!sub_inspector) {
				get_tree()->disconnect("node_removed", callable_mp(this, &EditorInspector::_node_removed));
			}
			edit(nullptr);
		} break;
		case NOTIFICATION_VISIBILITY_CHANGED: {
			set_process(is_visible_in_tree());
		} break;
		case NOTIFICATION_PROCESS: {
			if (update_scroll_request >= 0) {
				get_v_scroll_bar()->call_deferred(SNAME("set_value"), update_scroll_request);
				update_scroll_request = -1;
			}
			if (update_tree_pending) {
				refresh_countdown = float(EDITOR_GET("docks/property_editor/auto_refresh_interval"));
			} else if (refresh_countdown > 0) {
				refresh_countdown -= get_process_delta_time();
				if (refresh_countdown <= 0) {
					for (const KeyValue<StringName, List<EditorProperty *>> &F : editor_property_map) {
						for (EditorProperty *E : F.value) {
							if (E && !E->is_cache_valid()) {
								E->update_property();
								E->update_editor_property_status();
								E->update_cache();
							}
						}
					}
					refresh_countdown = float(EDITOR_GET("docks/property_editor/auto_refresh_interval"));
				}