### 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.

ERR_FAIL_COND(!nodes.has(p_node));
	nodes[p_node].connections.resize(nodes[p_node].node->get_input_count());
	emit_signal(SNAME("node_changed"), p_node);
}
void AnimationNodeBlendTree::_bind_methods() {
	ClassDB::bind_method(D_METHOD("add_node", "name", "node", "position"), &AnimationNodeBlendTree::add_node, DEFVAL(Vector2()));
	ClassDB::bind_method(D_METHOD("get_node", "name"), &AnimationNodeBlendTree::get_node);
	ClassDB::bind_method(D_METHOD("remove_node", "name"), &AnimationNodeBlendTree::remove_node);
	ClassDB::bind_method(D_METHOD("rename_node", "name", "new_name"), &AnimationNodeBlendTree::rename_node);
	ClassDB::bind_method(D_METHOD("has_node", "name"), &AnimationNodeBlendTree::has_node);
	ClassDB::bind_method(D_METHOD("connect_node", "input_node", "input_index", "output_node"), &AnimationNodeBlendTree::connect_node);
	ClassDB::bind_method(D_METHOD("disconnect_node", "input_node", "input_index"), &AnimationNodeBlendTree::disconnect_node);
	ClassDB::bind_method(D_METHOD("set_node_position", "name", "position"), &AnimationNodeBlendTree::set_node_position);
	ClassDB::bind_method(D_METHOD("get_node_position", "name"), &AnimationNodeBlendTree::get_node_position);
	ClassDB::bind_method(D_METHOD("set_graph_offset", "offset"), &AnimationNodeBlendTree::set_graph_offset);
	ClassDB::bind_method(D_METHOD("get_graph_offset"), &AnimationNodeBlendTree::get_graph_offset);
	ADD_PROPERTY(PropertyInfo(Variant::VECTOR2, "graph_offset", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NO_EDITOR), "set_graph_offset", "get_graph_offset");
	BIND_CONSTANT(CONNECTION_OK);
	BIND_CONSTANT(CONNECTION_ERROR_NO_INPUT);
	BIND_CONSTANT(CONNECTION_ERROR_NO_INPUT_INDEX);
	BIND_CONSTANT(CONNECTION_ERROR_NO_OUTPUT);
	BIND_CONSTANT(CONNECTION_ERROR_SAME_NODE);
	BIND_CONSTANT(CONNECTION_ERROR_CONNECTION_EXISTS);
	ADD_SIGNAL(MethodInfo("node_changed", PropertyInfo(Variant::STRING_NAME, "node_name")));
}
void AnimationNodeBlendTree::_initialize_node_tree() {