### 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)

switch (p_what) {
		case NOTIFICATION_READY: {
			if (!Engine::get_singleton()->is_editor_hint() && animation_set.has(autoplay)) {
				set_active(true);
				play(autoplay);
				seek(0, true);
			}
		} break;
	}
}
void AnimationPlayer::_process_playback_data(PlaybackData &cd, double p_delta, float p_blend, bool p_seeked, bool p_started, bool p_is_current) {
	double speed = speed_scale * cd.speed_scale;
	bool backwards = signbit(speed); 
	double delta = p_started ? 0 : p_delta * speed;
	double next_pos = cd.pos + delta;
	real_t len = cd.from->animation->get_length();
	Animation::LoopedFlag looped_flag = Animation::LOOPED_FLAG_NONE;
	switch (cd.from->animation->get_loop_mode()) {
		case Animation::LOOP_NONE: {
			if (next_pos < 0) {
				next_pos = 0;
			} else if (next_pos > len) {
				next_pos = len;
			}