### Godot version

4.2.beta.custom_build [51f81e1c8]

### System information

macOS 11.0+

### Issue description

I could sense a recent merging of a few pull requests on here:

<img width="865" alt="image" src="https://github.com/godotengine/godot/assets/1129695/1cf7d144-a4d2-4514-abca-1405222e702a">

This bug has the following related merges as the most recent ones:

https://github.com/godotengine/godot/pull/80813
https://github.com/godotengine/godot/pull/80939

The pull requests are for reviving onion-skinning capabilities, but this causes a minor unexpected result (see Steps to reproduce)



### Steps to reproduce

## A. Use 4.2.beta.custom_build [51f81e1c8]

1. Obtain the attached minimal reproduction project
2. Select the AnimationPlayer node
<img width="1468" alt="image" src="https://github.com/godotengine/godot/assets/1129695/ca16d7a6-7690-45b4-b8f9-b12fded64ca4">
3. In the Animation panel, click "Edit" to find your shortcuts for "Go to Next Step" and "Go to Previous Step"
<img width="410" alt="image" src="https://github.com/godotengine/godot/assets/1129695/a708e196-2eb9-42ea-bf0e-fd0aa88a9e60">
4. Use the shortcuts to spam go back and forth the animation

Expected result: animation goes smoothly

https://github.com/godotengine/godot/assets/1129695/c24c498c-7f77-4cc9-a1c9-a1627d89c58b



Actual result: animation jumps crazily


https://github.com/godotengine/godot/assets/1129695/947bf5b4-a0ab-42d4-bb5b-201800b4bdc6


https://github.com/godotengine/godot/assets/1129695/65303cd0-8c2d-4a35-9d16-c94752ac2e3a




## B. My successful yet unverified fix attempt on 4.2.beta.custom_build [51f81e1c8]

Either by:

<img width="831" alt="image" src="https://github.com/godotengine/godot/assets/1129695/80d167ae-27e7-4ec4-a4c9-ffc7adc0353f">


Or by:

<img width="806" alt="image" src="https://github.com/godotengine/godot/assets/1129695/2bae8697-8ef3-48dc-9f0a-2b5fe568ed43">


I don't see any negative impact on Onion Skinning or other functions by the above fix attempt, but I am not sure, I need someone to help me verify this.



### Minimal reproduction project

[gd_anim_unittest_1.zip](https://github.com/godotengine/godot/files/12909805/gd_anim_unittest_1.zip)






int count = 1;
	String base = "new_animation";
	String current_library_name = "";
	if (animation->has_selectable_items()) {
		String current_animation_name = animation->get_item_text(animation->get_selected());
		Ref<Animation> current_animation = player->get_animation(current_animation_name);
		if (current_animation.is_valid()) {
			current_library_name = player->find_animation_library(current_animation);
		}
	}
	String attempt_prefix = (current_library_name == "") ? "" : current_library_name + "/";
	while (true) {
		String attempt = base;
		if (count > 1) {
			attempt += vformat("_%d", count);
		}
		if (player->has_animation(attempt_prefix + attempt)) {
			count++;
			continue;
		}
		base = attempt;
		break;
	}
	_update_name_dialog_library_dropdown();
	name_dialog_op = TOOL_NEW_ANIM;
	name_dialog->set_title(TTR("Create New Animation"));
	name_dialog->popup_centered(Size2(300, 90));
	name_title->set_text(TTR("New Animation Name:"));
	name->set_text(base);
	name->select_all();