### Godot version

4.2 RC2

### System information

Any

### Issue description

AnimationMixer separates the accuracy of how discrete keys are retrieved when seeking between internal seeking and external seeking. FYI: https://github.com/godotengine/godot/pull/80708.

Since AnimationPlayer currently treats everything as an internal seek, so it needs to propagate the external seek information.

### Steps to reproduce

Seek AnimationTrackEditor

### Minimal reproduction project

[gd_anim_unittest_1.zip](https://github.com/godotengine/godot/files/13492063/gd_anim_unittest_1.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;
		}
	}