### Godot version

4.2

### System information

Linux

### Issue description

A nested state machine isn't traveling to its animation in `_ready()` in 4.2 as it was in 4.1.3.

In the ready function, we make the `root` state machine travel to the state of the `Stages` nested state machine. Then we immediately call the `Stages` nested state machine to travel to `Stage2`. This works fine in Godot v4.1.3, but not in Godot v4.2, where it seems a delay is first needed for the second travel animation to work.

![image](https://github.com/godotengine/godot/assets/788630/f1582a99-a68e-45d9-82b8-8367e62a9cba)
![image](https://github.com/godotengine/godot/assets/788630/c7c1f9fa-c78b-4259-bd36-81ebd8cef9aa)

### Steps to reproduce

Run the MRP below in 4.1.3 and 4.2.

In 4.1.3, the animation tree will reach `Stage2` and show Finished on the screen.

In 4.2, the animation tree will only reach `Stage1` and show Stuck on the screen.

### Minimal reproduction project

[MRP-AnimationNodeStateMachinePlayback.zip](https://github.com/godotengine/godot/files/13533132/MRP-AnimationNodeStateMachinePlayback.zip)

GDCLASS(AnimationNode, Resource);
public:
	friend class AnimationTree;
	enum FilterAction {
		FILTER_IGNORE,
		FILTER_PASS,
		FILTER_STOP,
		FILTER_BLEND
	};
	struct Input {
		String name;
	};
	bool closable = false;
	Vector<Input> inputs;
	HashMap<NodePath, bool> filter;
	bool filter_enabled = false;
	
	struct NodeState {
		StringName base_path;
		AnimationNode *parent = nullptr;
		Vector<StringName> connections;
		Vector<real_t> track_weights;
	} node_state;
	
	struct ProcessState {
		AnimationTree *tree = nullptr;
		HashMap<NodePath, int> track_map; 
		bool is_testing = false;
		bool valid = false;
		String invalid_reasons;