### Godot version

4.2 RC2

### System information

Any

### Issue description

AnimationMixer separates the accuracy of how discrete keys are retrieved when seeking between internal seeking and external seeking. FYI: https://github.com/godotengine/godot/pull/80708.

Since AnimationPlayer currently treats everything as an internal seek, so it needs to propagate the external seek information.

### Steps to reproduce

Seek AnimationTrackEditor

### Minimal reproduction project

[gd_anim_unittest_1.zip](https://github.com/godotengine/godot/files/13492063/gd_anim_unittest_1.zip)

_check_immediately_after_start();
	AnimationMixer::advance(p_time);
}
void AnimationPlayer::_check_immediately_after_start() {
	if (playback.started) {
		_process_animation(0); 
	}
}
bool AnimationPlayer::is_valid() const {
	return (playback.current.from);
}
double AnimationPlayer::get_current_animation_position() const {
	ERR_FAIL_NULL_V_MSG(playback.current.from, 0, "AnimationPlayer has no current animation.");
	return playback.current.pos;
}
double AnimationPlayer::get_current_animation_length() const {
	ERR_FAIL_NULL_V_MSG(playback.current.from, 0, "AnimationPlayer has no current animation.");
	return playback.current.from->animation->get_length();
}
void AnimationPlayer::set_autoplay(const String &p_name) {
	if (is_inside_tree() && !Engine::get_singleton()->is_editor_hint()) {
		WARN_PRINT("Setting autoplay after the node has been added to the scene has no effect.");
	}
	autoplay = p_name;
}
String AnimationPlayer::get_autoplay() const {