FWIW, I think your original problem is solved by adding :payload to the list of metadata values. I tried in a new mix project (with mix new), and the log output contained the payload as expected.
I think the Mix.install/2 version doesn’t work, because the Logger config you’re trying to set is part of the boot configuration (which is different from the compile configuration). Both can be set in config/config.exs, but I don’t know how that works with the Mix.install/2 way of configuring things. Maybe that’s just too late to influence the Logger’s boot configuration.
I’ve actually never thought about this “boot configuration” aspect of an Elixir app. So if anyone can chime in… Please do!
PS: just to be clear, this is the config that works, defined in config/config.exs:
# config/config.exs (or config/dev.exs)
config :logger, :console, # :default_handler also works
format: "[$level] $message $metadata\n",
metadata: [:payload]
# iex
require Logger
Logger.info("some message", payload: "some payload")
# > [info] some message payload=some payload
