### 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)

node_state.connections.clear();
	return _blend_node(p_node, p_subpath, this, p_playback_info, p_filter, p_sync, p_test_only, nullptr);
}
double AnimationNode::_blend_node(Ref<AnimationNode> p_node, const StringName &p_subpath, AnimationNode *p_new_parent, AnimationMixer::PlaybackInfo p_playback_info, FilterAction p_filter, bool p_sync, bool p_test_only, real_t *r_activity) {
	ERR_FAIL_COND_V(!p_node.is_valid(), 0);
	ERR_FAIL_NULL_V(process_state, 0);
	int blend_count = node_state.track_weights.size();
	if (p_node->node_state.track_weights.size() != blend_count) {
		p_node->node_state.track_weights.resize(blend_count);
	}
	real_t *blendw = p_node->node_state.track_weights.ptrw();
	const real_t *blendr = node_state.track_weights.ptr();
	bool any_valid = false;
	if (has_filter() && is_filter_enabled() && p_filter != FILTER_IGNORE) {
		for (int i = 0; i < blend_count; i++) {
			blendw[i] = 0.0; // 
		}
		for (const KeyValue<NodePath, bool> &E : filter) {
			if (!process_state->track_map.has(E.key)) {
				continue;
			}
			int idx = process_state->track_map[E.key];
			blendw[idx] = 1.0; // 
		}
		switch (p_filter) {
			case FILTER_IGNORE:
				break; //