### 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)

ClassDB::bind_method(D_METHOD("clear_queue"), &AnimationPlayer::clear_queue);
	ClassDB::bind_method(D_METHOD("set_speed_scale", "speed"), &AnimationPlayer::set_speed_scale);
	ClassDB::bind_method(D_METHOD("get_speed_scale"), &AnimationPlayer::get_speed_scale);
	ClassDB::bind_method(D_METHOD("get_playing_speed"), &AnimationPlayer::get_playing_speed);
	ClassDB::bind_method(D_METHOD("set_autoplay", "name"), &AnimationPlayer::set_autoplay);
	ClassDB::bind_method(D_METHOD("get_autoplay"), &AnimationPlayer::get_autoplay);
	ClassDB::bind_method(D_METHOD("find_animation", "animation"), &AnimationPlayer::find_animation);
	ClassDB::bind_method(D_METHOD("find_animation_library", "animation"), &AnimationPlayer::find_animation_library);
	ClassDB::bind_method(D_METHOD("set_movie_quit_on_finish_enabled", "enabled"), &AnimationPlayer::set_movie_quit_on_finish_enabled);
	ClassDB::bind_method(D_METHOD("is_movie_quit_on_finish_enabled"), &AnimationPlayer::is_movie_quit_on_finish_enabled);
	ClassDB::bind_method(D_METHOD("get_current_animation_position"), &AnimationPlayer::get_current_animation_position);
	ClassDB::bind_method(D_METHOD("get_current_animation_length"), &AnimationPlayer::get_current_animation_length);
	ClassDB::bind_method(D_METHOD("seek", "seconds", "update", "update_only"), &AnimationPlayer::seek, DEFVAL(false), DEFVAL(false));
	ADD_PROPERTY(PropertyInfo(Variant::STRING_NAME, "current_animation", PROPERTY_HINT_ENUM, "", PROPERTY_USAGE_EDITOR), "set_current_animation", "get_current_animation");
	ADD_PROPERTY(PropertyInfo(Variant::STRING_NAME, "assigned_animation", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE), "set_assigned_animation", "get_assigned_animation");
	ADD_PROPERTY(PropertyInfo(Variant::STRING_NAME, "autoplay", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NO_EDITOR), "set_autoplay", "get_autoplay");
	ADD_PROPERTY(PropertyInfo(Variant::FLOAT, "current_animation_length", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE), "", "get_current_animation_length");
	ADD_PROPERTY(PropertyInfo(Variant::FLOAT, "current_animation_position", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NONE), "", "get_current_animation_position");
	ADD_GROUP("Playback Options", "playback_");
	ADD_PROPERTY(PropertyInfo(Variant::FLOAT, "playback_default_blend_time", PROPERTY_HINT_RANGE, "0,4096,0.01,suffix:s"), "set_default_blend_time", "get_default_blend_time");
	ADD_PROPERTY(PropertyInfo(Variant::FLOAT, "speed_scale", PROPERTY_HINT_RANGE, "-4,4,0.001,or_less,or_greater"), "set_speed_scale", "get_speed_scale");
	ADD_PROPERTY(PropertyInfo(Variant::BOOL, "movie_quit_on_finish"), "set_movie_quit_on_finish_enabled", "is_movie_quit_on_finish_enabled");
	ADD_SIGNAL(MethodInfo(SNAME("current_animation_changed"), PropertyInfo(Variant::STRING, "name")));
	ADD_SIGNAL(MethodInfo(SNAME("animation_changed"), PropertyInfo(Variant::STRING_NAME, "old_name"), PropertyInfo(Variant::STRING_NAME, "new_name")));
}
AnimationPlayer::AnimationPlayer() {
}
AnimationPlayer::~AnimationPlayer() {
}