Trying to get custom field data in a simple plugin

You don’t have the $post object, but trying to use it in the code ($post->ID). Use get_the_ID() function instead:

<?php
while ( $cat_query->have_posts() ) : $cat_query->the_post();
    // $gread = get_post_meta( $post->ID, 'read_time', true );  // Wrong
    $gread = get_post_meta( get_the_ID(), 'read_time', true );      // Right
endwhile;

}

From now forth always enable debugging when you develop. In such a way you’ll avoid wasting your time and asking unpractical questions.