If you want to use a variable from a another context in a function, create a class:
class CustomLog
{
private $debug_msg = "";
public function __construct( $msg )
{
$this->debug_msg = $msg;
}
public function log()
{
error_log( $this->debug_msg, 0 );
}
}
add_action( 'init', [ new CustomLog( "Hi there!" ), 'log' ], 20 );
Now you can reuse the class multiple times for different messages and hooks.