### Godot version

4.1 dev3

### System information

Windows 11, Forward+, Intel 13700k, 4070ti

### Issue description

In 4.0.x and in 4.1 dev2, if you overwrite the rotation of a bone in `_process` it has preferred over the currently running animation. In 4.1 dev3, the running animation takes precedence and overwrites any changes in `_process`. This happens both with a simple animation and with an animation tree, and happens in-editor and in-game.

### Steps to reproduce

1. Open the attached project.
2. Click on `AnimationPlayer` and pick an animation, e.g. `Armature|Standing`. Set it to looping if it's not already. (@RandomShaper's note: and play it).
3. Click on the `PointOfInterest` and move it along the X axis.
4. If you're on:
    - 4.0.x or 4.1-dev2: Notice the head rotating
    - 4.1-dev3: Notice that nothing happens

### Minimal reproduction project

[BoneRotationIssue-4.0.3.zip](https://github.com/godotengine/godot/files/11582187/BoneRotationIssue-4.0.3.zip)
[BoneRotationIssue-4.1-dev.zip](https://github.com/godotengine/godot/files/11582188/BoneRotationIssue-4.1-dev.zip)


Should include all licensing stuff for the model, but let me just add [the link](https://opengameart.org/content/human-model-ready-for-animation) for good measure.
if (nodes_removed_on_group_call.has(gr_nodes[i])) {
				continue;
			}
			if (!(p_call_flags & GROUP_CALL_DEFERRED)) {
				gr_nodes[i]->notification(p_notification);
			} else {
				MessageQueue::get_singleton()->push_notification(gr_nodes[i], p_notification);
			}
		}
	} else {
		for (int i = 0; i < gr_node_count; i++) {
			if (nodes_removed_on_group_call.has(gr_nodes[i])) {
				continue;
			}
			if (!(p_call_flags & GROUP_CALL_DEFERRED)) {
				gr_nodes[i]->notification(p_notification);
			} else {
				MessageQueue::get_singleton()->push_notification(gr_nodes[i], p_notification);
			}
		}
	}
	{
		_THREAD_SAFE_METHOD_
		nodes_removed_on_group_call_lock--;
		if (nodes_removed_on_group_call_lock == 0) {
			nodes_removed_on_group_call.clear();
		}
	}
}
void SceneTree::set_group_flags(uint32_t p_call_flags, const StringName &p_group, const String &p_name, const Variant &p_value) {