### Godot version

v4.1.beta1.mono.official [828ec2c5d]

### System information

Godot v4.1.beta1.mono - Windows 10.0.22621 - Vulkan (Forward+) - dedicated NVIDIA GeForce RTX 4070 Ti (NVIDIA; 31.0.15.3598) - 13th Gen Intel(R) Core(TM) i5-13600K (20 Threads)

### Issue description

After the recent refactoring (https://github.com/godotengine/godot/pull/75901), Node process priority seems to be unimplemented. `ComparatorWithPriority` is no longer used anywhere in the engine code.

Nodes behave as if they all had the same priority, and running with `--single-threaded-scene` makes no difference.

### Steps to reproduce

Run the MRP, look at the order in which the nodes print their names.

In Godot 4.0.3: First, Default, Last
In Godot 4.1-beta1: Default, First, Last

### Minimal reproduction project

[ProcessPriorityBug.zip](https://github.com/godotengine/godot/files/11693028/ProcessPriorityBug.zip)

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 {