### Godot version

4.2 1ba920f

### System information

Windows 10.0.19045 - Vulkan (Forward+) - dedicated NVIDIA GeForce GTX 1060 (NVIDIA; 30.0.15.1403) - Intel(R) Core(TM) i7-7700HQ CPU @ 2.80GHz (8 Threads)

### Issue description

```GDScript
func _ready() -> void:
	$AnimationPlayer.play("new_animation")
	$AnimationPlayer.advance(0)
```
The animation has a single track with Update Mode set to discrete. It does not play, no matter the argument used.
Removing `advance()` will make it play.

Works correctly in rc1.

### Steps to reproduce

1. Run MRP on master
2. Run MRP in 4.2 rc1

### Minimal reproduction project

[brokedvance.zip](https://github.com/godotengine/godot/files/13460977/brokedvance.zip)

AnimationMixer::_rename_animation(p_from_name, p_to_name);
	
	List<BlendKey> to_erase;
	HashMap<BlendKey, double, BlendKey> to_insert;
	for (const KeyValue<BlendKey, double> &E : blend_times) {
		BlendKey bk = E.key;
		BlendKey new_bk = bk;
		bool erase = false;
		if (bk.from == p_from_name) {
			new_bk.from = p_to_name;
			erase = true;
		}
		if (bk.to == p_from_name) {
			new_bk.to = p_to_name;
			erase = true;
		}
		if (erase) {
			to_erase.push_back(bk);
			to_insert[new_bk] = E.value;
		}
	}