### 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)

p_group->call_queue.flush(); 
	Vector<Node *> &nodes = p_physics ? p_group->physics_nodes : p_group->nodes;
	if (nodes.is_empty()) {
		return;
	}
	bool &node_order_dirty = p_physics ? p_group->physics_node_order_dirty : p_group->node_order_dirty;
	if (node_order_dirty) {
		nodes.sort_custom<Node::ComparatorWithPhysicsPriority>();
		node_order_dirty = false;
	}
	
	Vector<Node *> nodes_copy = nodes;
	uint32_t node_count = nodes_copy.size();
	Node **nodes_ptr = (Node **)nodes_copy.ptr(); 
	for (uint32_t i = 0; i < node_count; i++) {
		Node *n = nodes_ptr[i];
		if (nodes_removed_on_group_call.has(n)) {
			
			
			continue;
		}
		if (!n->can_process() || !n->is_inside_tree()) {
			continue;
		}
		if (p_physics) {
			if (n->is_physics_processing()) {
				n->notification(Node::NOTIFICATION_PHYSICS_PROCESS);
			}