application.ex

defmodule MyApp.Application do
  # See https://hexdocs.pm/elixir/Application.html
  # for more information on OTP Applications
  @moduledoc false

  use Application
  use Supervisor

  def start(_type, _args) do
    children = [
      # Only children automatically started are required for all operation
      # modes- otherwise use start_/1 functions
      supervisor(MyApp.Repo, []),
    ]
    opts = [strategy: :one_for_one, name: __MODULE__]
    Supervisor.start_link(children, opts)
  end

  def start_recorder, do: Supervisor.start_child(__MODULE__, {Task.Supervisor, name: MyApp.RecordingSupervisor})
  def start_metrics do
    Supervisor.start_child(__MODULE__, Plug.Adapters.Cowboy.child_spec(:http, MyApp.MetricsExporter, [], port: 50010))
  end

end

broken.ex

defmodule Mix.Tasks.Listen do
  use Mix.Task

  @shortdoc "Starts application with webserver and metrics"
  def run(_) do
    Application.ensure_all_started(:myapp)
    MyApp.Application.start_metrics()
    MyApp.Application.start_recorder()
    Process.sleep(:infinity)
  end
end

### inserts very slow, eventual timeout
14:28:52.090 [debug] QUERY OK db=3950.4ms decode=3.0ms

working.ex

defmodule Mix.Tasks.Listen do
  use Mix.Task

  @shortdoc "Starts application with webserver and metrics"
  def run(_) do
    Mix.Task.run "app.start"
    MyApp.Application.start_metrics()
    MyApp.Application.start_recorder()
    Process.sleep(:infinity)
  end
end

### inserts work ok
14:26:25.285 [debug] QUERY OK db=3.6ms