### 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)

#include "animation_node_state_machine.h"
#include "scene/main/window.h"
void AnimationNodeStateMachineTransition::set_switch_mode(SwitchMode p_mode) {
	switch_mode = p_mode;
}
AnimationNodeStateMachineTransition::SwitchMode AnimationNodeStateMachineTransition::get_switch_mode() const {
	return switch_mode;
}
void AnimationNodeStateMachineTransition::set_advance_mode(AdvanceMode p_mode) {
	advance_mode = p_mode;
}
AnimationNodeStateMachineTransition::AdvanceMode AnimationNodeStateMachineTransition::get_advance_mode() const {
	return advance_mode;
}
void AnimationNodeStateMachineTransition::set_advance_condition(const StringName &p_condition) {
	String cs = p_condition;
	ERR_FAIL_COND(cs.contains("/") || cs.contains(":"));
	advance_condition = p_condition;
	if (!cs.is_empty()) {
		advance_condition_name = "conditions/" + cs;
	} else {
		advance_condition_name = StringName();
	}
	emit_signal(SNAME("advance_condition_changed"));
}
StringName AnimationNodeStateMachineTransition::get_advance_condition() const {