### 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.

real_t blend_inv = 1.0;
		bool use_blend = sync;
		if (xfade_time > 0) {
			use_blend = true;
			blend = cur_prev_xfading / xfade_time;
			if (xfade_curve.is_valid()) {
				blend = xfade_curve->sample(blend);
			}
			blend_inv = 1.0 - blend;
			blend = Math::is_zero_approx(blend) ? CMP_EPSILON : blend;
			blend_inv = Math::is_zero_approx(blend_inv) ? CMP_EPSILON : blend_inv;
		}
		
		if (input_data[cur_current_index].reset && !p_seek && switched) { 
			rem = blend_input(cur_current_index, 0, true, p_is_external_seeking, blend_inv, FILTER_IGNORE, true, p_test_only);
		} else {
			rem = blend_input(cur_current_index, p_time, p_seek, p_is_external_seeking, blend_inv, FILTER_IGNORE, true, p_test_only);
		}
		blend_input(cur_prev_index, p_time, use_blend && p_seek, p_is_external_seeking, blend, FILTER_IGNORE, true, p_test_only);
		if (p_seek) {
			cur_time = abs_time;
		} else {
			cur_time += abs_time;
			cur_prev_xfading -= abs_time;
			if (cur_prev_xfading < 0) {
				set_parameter(prev_index, -1);
			}
		}
	}
	set_parameter(time, cur_time);