I see. As you already may have guessed, that’s a different part of the API and can’t be done while creating an issue. It requires a different set of permissions. And this part is undergoing a bit of recent change. As such, you’ll find both deprecated endpoints and new experimental ones.
In your case, I recommend Update custom field options (context) using PUT /rest/api/3/field/{fieldId}/context/{contextId}/option. If you have any problems applying that new documentation, please let us know; it’s a great opportunity for us to make it better for everyone.