### 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.

set_parameter(request, ONE_SHOT_REQUEST_NONE);
		set_parameter(internal_active, true);
		set_parameter(active, true);
	}
	real_t blend = 1.0;
	bool use_blend = sync;
	if (cur_time < fade_in) {
		if (fade_in > 0) {
			use_blend = true;
			blend = cur_time / fade_in;
			if (fade_in_curve.is_valid()) {
				blend = fade_in_curve->sample(blend);
			}
		} else {
			blend = 0; 
		}
	} else if (!do_start && !is_fading_out && cur_remaining <= fade_out) {
		is_fading_out = true;
		cur_fade_out_remaining = cur_remaining;
		set_parameter(internal_active, false);
	}
	if (is_fading_out) {
		use_blend = true;
		if (fade_out > 0) {
			blend = cur_fade_out_remaining / fade_out;
			if (fade_out_curve.is_valid()) {
				blend = 1.0 - fade_out_curve->sample(1.0 - blend);
			}
		} else {
			blend = 0;