Echo custom admin field into a is_single()

$postids = get_option('codeable_posts_field');

This will give you a string of comma separated post ids (according to your code, and if the user follows the instructions).

array( $postids )

will turn it into an array with that string as the only element. That won’t work with is_single(), obviously, because is_single doesn’t do any further splitting.

Here’s how to turn that string into a proper array using preg_split. Replace

$postids = get_option('codeable_posts_field');

with

$postids = preg_split("/\s*,\s*/", get_option('codeable_posts_field'));

preg_split uses a regular expression to split a string into an array. I’ve added \s* before and after the comma so that it will work for 123,456 and also for 123, 456 or 123 , 456.

With $postids being an array, your check should work just fine. If it doesn’t, try

var_export($postids);

to see what $postids really contains.