### Godot version

v4.1.1.stable.official [bd6af8e0e]

### System information

Godot v4.1.1.stable - Windows 10.0.19045 - Vulkan (Forward+) - dedicated NVIDIA GeForce GTX 1060 6GB (NVIDIA; 31.0.15.3179) - Intel(R) Core(TM) i5-8500 CPU @ 3.00GHz (6 Threads)

### Issue description

When connecting the `animation_started` signal from an animation tree, the connected method is always called twice.
This only occurs with the `animation_started` signal, the `animation_finished` signal is only emitted once.

This unfortunately makes relying on the signal impossible.

### Steps to reproduce

(See minimal production project)
- Use `animation_started.connect()`
- Print something out in the connected method (the example project prints the `anim_name` parameter)
- method is called twice -> two prints in the console

### Minimal reproduction project

[anim_tree_signal_bug.zip](https://github.com/godotengine/godot/files/12229864/anim_tree_signal_bug.zip)

The animation tree travels to the 'move' animation when `ui_accept` is pressed (see `anim_tree.gd`) and has print statements inside the methods connected to both the `animation_started` and `animation_finished` signal.

}
			}
		}
		
		
		if (state->tree) {
			
			if (p_seek && !p_is_external_seeking && cur_time == 0) {
				state->tree->call_deferred(SNAME("emit_signal"), "animation_started", animation);
			}
			
			if (prev_time < anim_size && cur_time >= anim_size) {
				state->tree->call_deferred(SNAME("emit_signal"), "animation_finished", animation);
			}
		}
	}
	if (!p_test_only) {
		if (play_mode == PLAY_MODE_FORWARD) {
			blend_animation(animation, cur_time, step, p_seek, p_is_external_seeking, 1.0, looped_flag);
		} else {
			blend_animation(animation, anim_size - cur_time, -step, p_seek, p_is_external_seeking, 1.0, looped_flag);
		}
	}
	set_parameter(time, cur_time);
	return is_looping ? HUGE_LENGTH : anim_size - cur_time;
}
String AnimationNodeAnimation::get_caption() const {
	return "Animation";
}
void AnimationNodeAnimation::set_play_mode(PlayMode p_play_mode) {