FYI:

       spawn fn ->
         IO.puts("====================== sleep start")
        Process.sleep(5000)
         IO.puts("====================== sleep over")
         \< update socket state here \>
       end

The whole \< update socket state here \> bit was never going to work, even if did all of this in the parent live view. You can send the live view a message and have it update the socket there, but the socket is immutable, and can’t be changed in another process at all.

Perhaps a relatively simple solution could look like this:

live_component(YourComponent, %{
... other assigns
done: @done_components[id-of-component]
})

  # in your livesocket
  def update(params, socket) do
     # The parent live view is telling this live component that it has timed out, react accordingly.
     if params.done do
     end
  end

  def handle_event("patch_received", patch, socket) do
    socket = assign(socket, :import, %{socket.assigns.import | count: socket.assigns.import.count + 1})
    socket = reset_timer(socket)
    {:noreply, socket}
  end

  defp timer(socket) do
    Process.cancel_timer(socket.assigns.timer_ref)
    # clear out the timeout. This is important because technically the timer could have fired 
    # right as we canceled it.
    id = socket.assigns.id
    receive do
      {:timeout, ^id} -> :ok
    after
      0 -> :ok
    end
    # Send ourselves a message in 5 seconds with the id of the live socket
    Process.send_after(self, {:timeout, socket.assigns.id}, 5_000)
  end

Then in the live view we just need to handle the message and set the done flag properly:

# in the live view
# you also need to initialize :done_components on mount to `%{}`
def handle_info({:timeout, component_id}, socket) do
  socket = update(socket, :done_components, fn done_components ->
    Map.put(done_components, component_id, true)
  end)
  {:noreply, socket}
end

Basically, the idea is this. The live component manages the timeout timer, canceling it and restarting it if you get a payload. If the timeout timer is allowed to fire it sends a message to the actual live view, which essentially “routes” that fact to the live component via the params to the live component.