I’ve now implemented it:

defmodule Myapp.RequestTimeout do
  use GenServer

  require Logger

  @timeout :timer.seconds(2)

  def start_link(_) do
    GenServer.start_link(__MODULE__, %{}, name: __MODULE__)
  end

  @impl true
  def init(_) do
    {:ok, nil}
  end

  @impl true
  def handle_cast({:register_request, log_meta, request_pid}, state) do
    Process.send_after(__MODULE__, {:kill_if_open, log_meta, request_pid}, @timeout)
    {:noreply, state}
  end

  @impl true
  def handle_info({:kill_if_open, log_meta, request_pid}, state) do
    Logger.metadata(log_meta)

    Logger.error("RequestTimeoutError: #{Logger.metadata()[:request_id]}")

    Process.exit(request_pid, :timeout)

    {:noreply, state}
  end

  #
  # API
  #

  def register_request(log_meta) do
    GenServer.cast(__MODULE__, {:register_request, log_meta, self()})
  end
end

defmodule Myapp.RequestTimeout.Plug do
  def init(opts) do
    opts
  end

  def call(conn, _) do
    IO.inspect(Logger.metadata()[:request_id], label: "request_id")

    Myapp.RequestTimeout.register_request(Logger.metadata())

    conn
  end
end

But there is no response sent to the user, the browser just hangs.

If anyone has any feedback or suggestions I’d be grateful to hear.

Thanks