identified performance issues with streamed markdown

lib/elixir_ai_web/live/home_live.ex

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+defmodule ElixirAiWeb.HomeLive do
+  use ElixirAiWeb, :live_view
+  alias ElixirAi.ConversationManager
+
+  def mount(_params, _session, socket) do
+    {:ok,
+     socket
+     |> assign(conversations: ConversationManager.list_conversations())
+     |> assign(new_name: "")
+     |> assign(error: nil)}
+  end
+
+  def render(assigns) do
+    ~H"""
+    <div class="max-w-lg mx-auto mt-16 px-4">
+      <h1 class="text-lg font-semibold text-cyan-300 mb-8">Conversations</h1>
+
+      <ul class="mb-8 space-y-2">
+        <%= if @conversations == [] do %>
+          <li class="text-sm text-cyan-700">No conversations yet.</li>
+        <% end %>
+        <%= for name <- @conversations do %>
+          <li>
+            <.link
+              navigate={~p"/chat/#{name}"}
+              class="block px-4 py-2 rounded-lg border border-cyan-900/40 bg-cyan-950/20 text-cyan-300 hover:border-cyan-700 hover:bg-cyan-950/40 transition-colors text-sm"
+            >
+              {name}
+            </.link>
+          </li>
+        <% end %>
+      </ul>
+
+      <form phx-submit="create" class="flex gap-2">
+        <input
+          type="text"
+          name="name"
+          value={@new_name}
+          placeholder="New conversation name"
+          class="flex-1 rounded px-3 py-2 text-sm bg-cyan-950/20 border border-cyan-900/40 text-cyan-100 placeholder-cyan-800 focus:outline-none focus:ring-1 focus:ring-cyan-700"
+          autocomplete="off"
+        />
+        <button
+          type="submit"
+          class="px-4 py-2 rounded text-sm border border-cyan-900/40 bg-cyan-950/20 text-cyan-300 hover:border-cyan-700 hover:bg-cyan-950/40 transition-colors"
+        >
+          Create
+        </button>
+      </form>
+
+      <%= if @error do %>
+        <p class="mt-2 text-sm text-red-400">{@error}</p>
+      <% end %>
+    </div>
+    """
+  end
+
+  @spec handle_event(<<_::48>>, map(), any()) :: {:noreply, any()}
+  def handle_event("create", %{"name" => name}, socket) do
+    name = String.trim(name)
+
+    if name == "" do
+      {:noreply, assign(socket, error: "Name can't be blank")}
+    else
+      case ConversationManager.create_conversation(name) do
+        {:ok, _pid} ->
+          {:noreply,
+           socket
+           |> push_navigate(to: ~p"/chat/#{name}")
+           |> assign(error: nil)}
+
+        {:error, :already_exists} ->
+          {:noreply, assign(socket, error: "A conversation with that name already exists")}
+
+        _ ->
+          {:noreply, assign(socket, error: "Failed to create conversation")}
+      end
+    end
+  end
+end