This is exactly the right approach. Not sure why your codebase diverged from that, but here are the relevant fragments from a freshly generated Phoenix API project (--no-html --no-webpack):

# config/dev.exs
config :test, TestWeb.Endpoint,
  render_errors: [view: TestWeb.ErrorView, accepts: ~w(json), layout: false],
  # ...

# lib/test_web/views/error_view.ex
defmodule TestWeb.ErrorView do
  use TestWeb, :view

  # If you want to customize a particular status code
  # for a certain format, you may uncomment below.
  # def render("500.json", _assigns) do
  #   %{errors: %{detail: "Internal Server Error"}}
  # end

  # By default, Phoenix returns the status message from
  # the template name. For example, "404.json" becomes
  # "Not Found".
  def template_not_found(template, _assigns) do
    %{errors: %{detail: Phoenix.Controller.status_message_from_template(template)}}
  end
end