選択する必要のあるオプションは$print_version1[array_keys($ print_version1)[0]
だと思いますwhile ($row = $result->fetch_assoc()) {
$nx_version = $row['nx_version'];
if($_SESSION["id"]) {
if($nx_version == "the hardcode value you want to be selected"){
echo '<option selected="selected">'.$nx_version.'</option>';
}else{
echo '<option>'.$nx_version.'</option>';
}
}else{
if($print_version1[array_keys($print_version1)[0]] == $nx_version){
echo '<option selected="selected">'.$nx_version.'</option>';
}else{
echo '<option>'.$nx_version.'</option>';
}
}
}