### 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.
return current_frame;
}
TypedArray<Node> SceneTree::_get_nodes_in_group(const StringName &p_group) {
	_THREAD_SAFE_METHOD_
	TypedArray<Node> ret;
	HashMap<StringName, Group>::Iterator E = group_map.find(p_group);
	if (!E) {
		return ret;
	}
	_update_group_order(E->value); 
	int nc = E->value.nodes.size();
	if (nc == 0) {
		return ret;
	}
	ret.resize(nc);
	Node **ptr = E->value.nodes.ptrw();
	for (int i = 0; i < nc; i++) {
		ret[i] = ptr[i];
	}
	return ret;
}
bool SceneTree::has_group(const StringName &p_identifier) const {