### 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.
nodes_removed_on_group_call_lock++;
	}
	Vector<ObjectID> no_context_node_ids; 
	for (int i = gr_node_count - 1; i >= 0; i--) {
		if (p_viewport->is_input_handled()) {
			break;
		}
		Node *n = gr_nodes[i];
		if (nodes_removed_on_group_call.has(n)) {
			continue;
		}
		if (!n->can_process()) {
			continue;
		}
		switch (p_call_type) {
			case CALL_INPUT_TYPE_INPUT:
				n->_call_input(p_input);
				break;
			case CALL_INPUT_TYPE_SHORTCUT_INPUT: {
				const Control *c = Object::cast_to<Control>(n);
				if (c) {
					
					
					if (c->get_shortcut_context() == nullptr) {
						no_context_node_ids.append(n->get_instance_id());
						continue;
					}
					if (!c->is_focus_owner_in_shortcut_context()) {
						continue;
					}