share provider connection logic between setup wizard and providers form

Extract Products.connect_provider/2 that tests the connection, fetches
shop_id, creates the record, and enqueues sync. Both the setup wizard
and the providers form now use this shared function instead of
duplicating the flow. Also makes the products empty state context-aware
(distinguishes "no provider" from "provider connected but no products").

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

lib/berrypod/products.ex

@@ -64,6 +64,59 @@ defmodule Berrypod.Products do
     |> Repo.insert()
   end
 
+  @doc """
+  Tests an API key, creates the connection with config (shop_id etc),
+  and enqueues a product sync. Used by both setup wizard and providers form.
+
+  Returns `{:ok, connection}` or `{:error, reason}`.
+  """
+  def connect_provider(api_key, provider_type) do
+    alias Berrypod.Providers
+
+    encrypted =
+      case Berrypod.Vault.encrypt(api_key) do
+        {:ok, enc} -> enc
+        _ -> nil
+      end
+
+    temp_conn = %ProviderConnection{
+      provider_type: provider_type,
+      api_key_encrypted: encrypted
+    }
+
+    with {:ok, test_result} <- Providers.test_connection(temp_conn) do
+      name = provider_display_name(provider_type, test_result)
+      config = provider_config(provider_type, test_result)
+
+      params =
+        %{"api_key" => api_key, "provider_type" => provider_type, "name" => name}
+        |> then(fn p -> if config != %{}, do: Map.put(p, "config", config), else: p end)
+
+      case create_provider_connection(params) do
+        {:ok, connection} ->
+          enqueue_sync(connection)
+          {:ok, connection}
+
+        {:error, _} = error ->
+          error
+      end
+    end
+  end
+
+  defp provider_display_name("printify", %{shop_name: name}) when is_binary(name), do: name
+  defp provider_display_name("printful", %{store_name: name}) when is_binary(name), do: name
+
+  defp provider_display_name(type, _) do
+    case Berrypod.Providers.Provider.get(type) do
+      nil -> type
+      info -> info.name
+    end
+  end
+
+  defp provider_config("printify", %{shop_id: id}), do: %{"shop_id" => to_string(id)}
+  defp provider_config("printful", %{store_id: id}), do: %{"store_id" => to_string(id)}
+  defp provider_config(_, _), do: %{}
+
   @doc """
   Updates a provider connection.
   """