### 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)

is_grouped = p_is_grouped;
}
void AnimationNodeStateMachinePlayback::travel(const StringName &p_state, bool p_reset_on_teleport) {
	ERR_FAIL_COND_EDMSG(is_grouped, "Grouped AnimationNodeStateMachinePlayback must be handled by parent AnimationNodeStateMachinePlayback. You need to retrieve the parent Root/Nested AnimationNodeStateMachine.");
	ERR_FAIL_COND_EDMSG(String(p_state).contains("/Start") || String(p_state).contains("/End"), "Grouped AnimationNodeStateMachinePlayback doesn't allow to play Start/End directly. Instead, play the prev or next state of group in the parent AnimationNodeStateMachine.");
	_travel_main(p_state, p_reset_on_teleport);
}
void AnimationNodeStateMachinePlayback::start(const StringName &p_state, bool p_reset) {