### 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 (what == "node") {
			if (nodes.has(node_name)) {
				r_ret = nodes[node_name].node;
				return true;
			}
		}
		if (what == "position") {
			if (nodes.has(node_name)) {
				r_ret = nodes[node_name].position;
				return true;
			}
		}
	} else if (prop_name == "node_connections") {
		List<NodeConnection> nc;
		get_node_connections(&nc);
		Array conns;
		conns.resize(nc.size() * 3);
		int idx = 0;
		for (const NodeConnection &E : nc) {
			conns[idx * 3 + 0] = E.input_node;
			conns[idx * 3 + 1] = E.input_index;
			conns[idx * 3 + 2] = E.output_node;
			idx++;
		}
		r_ret = conns;
		return true;
	}
	return false;
}
void AnimationNodeBlendTree::_get_property_list(List<PropertyInfo> *p_list) const {