### 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(prev_xfading, cur_prev_xfading);
	return rem;
}
void AnimationNodeTransition::_get_property_list(List<PropertyInfo> *p_list) const {
	for (int i = 0; i < get_input_count(); i++) {
		p_list->push_back(PropertyInfo(Variant::STRING, "input_" + itos(i) + "/name", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_INTERNAL));
		p_list->push_back(PropertyInfo(Variant::BOOL, "input_" + itos(i) + "/auto_advance", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_INTERNAL));
		p_list->push_back(PropertyInfo(Variant::BOOL, "input_" + itos(i) + "/reset", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_INTERNAL));
	}
}
void AnimationNodeTransition::_bind_methods() {
	ClassDB::bind_method(D_METHOD("set_input_count", "input_count"), &AnimationNodeTransition::set_input_count);
	ClassDB::bind_method(D_METHOD("set_input_as_auto_advance", "input", "enable"), &AnimationNodeTransition::set_input_as_auto_advance);
	ClassDB::bind_method(D_METHOD("is_input_set_as_auto_advance", "input"), &AnimationNodeTransition::is_input_set_as_auto_advance);
	ClassDB::bind_method(D_METHOD("set_input_reset", "input", "enable"), &AnimationNodeTransition::set_input_reset);
	ClassDB::bind_method(D_METHOD("is_input_reset", "input"), &AnimationNodeTransition::is_input_reset);
	ClassDB::bind_method(D_METHOD("set_xfade_time", "time"), &AnimationNodeTransition::set_xfade_time);
	ClassDB::bind_method(D_METHOD("get_xfade_time"), &AnimationNodeTransition::get_xfade_time);
	ClassDB::bind_method(D_METHOD("set_xfade_curve", "curve"), &AnimationNodeTransition::set_xfade_curve);
	ClassDB::bind_method(D_METHOD("get_xfade_curve"), &AnimationNodeTransition::get_xfade_curve);
	ClassDB::bind_method(D_METHOD("set_allow_transition_to_self", "enable"), &AnimationNodeTransition::set_allow_transition_to_self);
	ClassDB::bind_method(D_METHOD("is_allow_transition_to_self"), &AnimationNodeTransition::is_allow_transition_to_self);
	ADD_PROPERTY(PropertyInfo(Variant::FLOAT, "xfade_time", PROPERTY_HINT_RANGE, "0,120,0.01,suffix:s"), "set_xfade_time", "get_xfade_time");
	ADD_PROPERTY(PropertyInfo(Variant::OBJECT, "xfade_curve", PROPERTY_HINT_RESOURCE_TYPE, "Curve"), "set_xfade_curve", "get_xfade_curve");
	ADD_PROPERTY(PropertyInfo(Variant::BOOL, "allow_transition_to_self"), "set_allow_transition_to_self", "is_allow_transition_to_self");
	ADD_PROPERTY(PropertyInfo(Variant::INT, "input_count", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_EDITOR | PROPERTY_USAGE_ARRAY | PROPERTY_USAGE_UPDATE_ALL_IF_MODIFIED, "Inputs,input_"), "set_input_count", "get_input_count");
}
AnimationNodeTransition::AnimationNodeTransition() {
}
String AnimationNodeOutput::get_caption() const {