### Godot version

4.2-rc1

### System information

Windows 11

### Issue description

The issue does not exist on Godot 4.1.3, only in 4.2

When you call `seek()` on the AnimationPlayer, the animation does not update instantly and freezes for a brief moment.
So if you need to switch multiple animations in a short amount of time while also calling `seek()`, the animation will just stop.

### Steps to reproduce

- Add a Sprite2D
- Set a spritesheet for the Sprite2D
- Add an AnimationPlayer
- Create a Property animation track and add some frames
- Loop the animation
- Create a different animation for the same sprite an loop it
- Switch between animations and call `seek()` when you do

### Minimal reproduction project

The included project demonstrates the issue perfectly (I know that calling `play()` and `seek()` on each `_process()` is a bit overkill, but it does allow for a better demonstration). The same project works perfectly in Godot 4.1.3.

[AnimationBug.zip](https://github.com/godotengine/godot/files/13400011/AnimationBug.zip)

Vector<String> get_queue();
	void clear_queue();
	void pause();
	void stop(bool p_keep_state = false);
	bool is_playing() const;
	String get_current_animation() const;
	void set_current_animation(const String &p_animation);
	String get_assigned_animation() const;
	void set_assigned_animation(const String &p_animation);
	bool is_valid() const;
	void set_speed_scale(float p_speed);
	float get_speed_scale() const;
	float get_playing_speed() const;
	void set_autoplay(const String &p_name);
	String get_autoplay() const;
	void set_movie_quit_on_finish_enabled(bool p_enabled);
	bool is_movie_quit_on_finish_enabled() const;
	void seek(double p_time, bool p_update = false, bool p_update_only = false);
	double get_current_animation_position() const;
	double get_current_animation_length() const;
	void get_argument_options(const StringName &p_function, int p_idx, List<String> *r_options) const override;
	AnimationPlayer();
	~AnimationPlayer();
};
#ifndef DISABLE_DEPRECATED
VARIANT_ENUM_CAST(AnimationPlayer::AnimationProcessCallback);
VARIANT_ENUM_CAST(AnimationPlayer::AnimationMethodCallMode);
#endif 
#endif