Well it looks like if I execute the following code:

<?php

$key = "0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF";
$v = pack("H*", $key);
file_put_contents("data", $v);

And the following elixir code:

packed = File.read!("data")
IO.inspect(packed, label: "packed")

I get the following output from elixir:

packed: <<1, 35, 69, 103, 137, 171, 205, 239, 1, 35, 69, 103, 137, 171, 205, 239, 1, 35,
  69, 103, 137, 171, 205, 239, 1, 35, 69, 103, 137, 171, 205, 239, 1, 35, 69,
  103, 137, 171, 205, 239, 1, 35, 69, 103, 137, 171, 205, 239, 1, 35, ...>>

And If I just decode the key I get this:

key = "0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF"
decoded = Base.decode16!(key)
IO.inspect(decoded, label: "decoded")

decoded: <<1, 35, 69, 103, 137, 171, 205, 239, 1, 35, 69, 103, 137, 171, 205, 239, 1, 35,
  69, 103, 137, 171, 205, 239, 1, 35, 69, 103, 137, 171, 205, 239, 1, 35, 69,
  103, 137, 171, 205, 239, 1, 35, 69, 103, 137, 171, 205, 239, 1, 35, ...>>

It seems that with H* pack() is just doing a decoding from base 16.

So maybe you should do something like that:

bin_key = Base.decode16!(hmac_key)
hmac =  Base.encode16(:crypto.mac(:hmac, :sha512, bin_key, msg))