### Godot version

4.2.rc1

### System information

win11

### Issue description
If you call animation.advance() after play() within a single process frame, the animation will not work properly.
The advance function does not work.
![image](https://github.com/godotengine/godot/assets/91177204/0edd6d63-9bfb-4860-8e14-1f0767bc4346)
The advance function does not work either.
![image](https://github.com/godotengine/godot/assets/91177204/fa5397d4-4615-44c9-aa7e-c2eae0e59a5f)
The advance function works, but 2 frames have already shown
![image](https://github.com/godotengine/godot/assets/91177204/c2df992a-ab64-43af-b9c7-89abb005b1c2)

This bug is not present in 4.1.3.stable.



### Steps to reproduce

create a scene with animation and run code like below.
```
func _ready():
	animation_player.play("new_animation")   
	animation_player.advance(5.0)
```
the advance function did nothing.

### Minimal reproduction project

[animation_play_advence.zip](https://github.com/godotengine/godot/files/13400233/animation_play_advence.zip)

AnimationMixer::_animation_removed(p_name, p_library);
	StringName name = p_library == StringName() ? p_name : StringName(String(p_library) + "/" + String(p_name));
	if (!animation_set.has(name)) {
		return; 
	}
	_animation_set_cache_update();
	
	List<BlendKey> to_erase;
	for (const KeyValue<BlendKey, double> &E : blend_times) {
		BlendKey bk = E.key;
		if (bk.from == name || bk.to == name) {
			to_erase.push_back(bk);
		}
	}
	while (to_erase.size()) {
		blend_times.erase(to_erase.front()->get());
		to_erase.pop_front();
	}
}
void AnimationPlayer::_rename_animation(const StringName &p_from_name, const StringName &p_to_name) {