The solution I found here is to open an interactive shell in the target directory, and grab the PATH from there. Afterwards I can call `:os.find_executable(~c"elixir", path)`:

shell = System.get_env("SHELL")

{path, 0} = System.cmd(shell, ["-i", "-l", "-c", "cd #{project_path} && echo $PATH"])
elixir_executable = :os.find_executable(~c"elixir", to_charlist(path))