Propagate logger metadata in spawned task

Not really. All approaches will effectively need the same approach. However I would do it like that:

metadata = :logger.get_process_metadata()

Task.Supervisor.start_child(fn ->
  :logger.set_process_metadata(metadata)
  my_task()
end)

So the my_task/0 will not need to know anything about logger metadata.

The reason why I use :logger API instead of Logger API is that using :logger directly do not require to change map to list and then list to map and instead just uses map directly.