What is the right way to broadcast a message with PubSub and receive with Channel

I have an Elixir 1.54 and Phoenix umbrella app containing:
[AdminWeb]
[Admin]
[DisplayWeb]

The [AdminWeb] calls a function defined in [Admin] that pulls information from a
Database, then converts it to a list of maps and should broadcast it to DisplayWeb channel:

[AdminWeb] → [Admin] → [DisplayWeb]

The code in [Admin] looks like this:

# news.ex

    def news_sort(id_list) do
        news_payload = news_items_from_db() |> struct_to_map()
        PubSub.broadcast(Admin.PubSub, "cast:news", news_payload)
    end

The code in [DisplayWeb] looks like this:

#news_channel.ex

  def join("cast:news", _payload, socket) do
    self() |> send({:after_join, "cast:news"})
    {:ok,socket}
  end

 def handle_info({:after_join, "cast:news"}, socket) do
    broadcast!(socket, "newscast", %{data: news_payload})
   {:noreply, socket}
 end

The PubSub.broadcast in [Admin] returns :ok message but the [DisplayWeb] does not receive any message. It neither works not returns any error message.

Please, what’s wrong with the code? What’s the right way to implement this solution?