I think I figured it out.

What I did was add a :other field to my metadata array, then i adde a case for my custom log formatter to handle that field.

So my config became like this:

config :logger, :console,
  level: :debug,
  metadata: [:other],
  format: {Log.Formatter, :format}

And my formatter like this:

defmodule Log.Formatter do
  @moduledoc false

  alias IO.ANSI

  @color_reset ANSI.reset()
  @highlight ANSI.light_magenta()

  def format(:debug, message, timestamp, metadata),
    do: format(:debug, message, timestamp, metadata, ANSI.cyan())

  def format(:info, message, timestamp, metadata),
    do: format(:info, message, timestamp, metadata, ANSI.green())

  def format(:notice, message, timestamp, metadata),
    do: format(:notice, message, timestamp, metadata, ANSI.light_yellow())

  def format(:warn, message, timestamp, metadata),
    do: format(:warn, message, timestamp, metadata, ANSI.yellow())

  def format(:warning, message, timestamp, metadata),
    do: format(:warn, message, timestamp, metadata, ANSI.yellow())

  def format(:error, message, timestamp, metadata),
    do: format(:error, message, timestamp, metadata, ANSI.red())

  def format(:critical, message, timestamp, metadata),
    do: format(:critical, message, timestamp, metadata, ANSI.yellow_background())

  def format(:alert, message, timestamp, metadata),
    do: format(:alert, message, timestamp, metadata, ANSI.light_red_background())

  def format(:emergency, message, timestamp, metadata),
    do: format(:emergency, message, timestamp, metadata, ANSI.red_background())

  defp format(level, message, timestamp, metadata, color) do
    date_time = format_date_time(timestamp)
    metadata = format_metadata(metadata, color)

    "\n#{color}#{date_time} [#{level}] #{metadata}\n↳ #{message}#{@color_reset}\n"
  rescue
    _ -> "Could not format message: #{inspect({level, message, timestamp, metadata})}"
  end

  # This is the function I added
  defp format_metadata([{:other, value} | rest], color) do
    "#{@highlight}#{inspect(value)}#{color} " <> format_metadata(rest, color)
  end

  defp format_metadata([{_key, value} | rest], color) do
    "#{inspect(value)} " <> format_metadata(rest, color)
  end

  defp format_metadata([], _), do: ""

  defp format_date_time({date, time}) do
    alias Logger.Formatter

    "#{Formatter.format_date(date)} #{Formatter.format_time(time)}"
  end
end

That way, I can send any data to it using the other metadata,

For example, Logger.error("blibs", other: %{blibs: 2}) will be logged as:

2025-07-14 19:23:44.530 [error] #PID<0.770.0> %{blibs: 2} 
↳ blibs