Local Post Date in WordPress Admin Panel Tables

Column filter:
The filter for modifying, removing or adding columns to post list in WordPress admin panel is manage_{$post_type}_posts_columns. Exchange {$post_type} with the desired post type. For example; if you want to edit columns for post type 'post', the filter name would be manage_post_posts_columns. And for a custom post type 'product', the filter name would be manage_product_posts_columns.

Column content hook:
The hook for controlling the output of the column content in WordPress admin panel is manage_{$post_type}_posts_custom_column with the desired post type. For example; if you want to edit columns for post type 'post', the filter name would be manage_post_posts_custom_column.

For your case you need to remove default date column and add your custom column with your local date. See the example code below for 'post' type.

// manage the columns of the `post` post type
function manage_columns_for_post($columns){
  //remove columns
  unset($columns['date']);
  
  //add new columns
  $columns['local_date'] = 'Local Date';
  
  return $columns; 
}

add_action('manage_post_posts_columns','manage_columns_for_post');

// populate custom columns for `post` post type
function populate_post_custom_columns($column,$post_id){

  //local date column
  if($column == 'local_date'){
    // convert date to local by $post_id
    echo 'Published <br> 2020/12/12 at 6:30 am'; // dynamically get date of each post and display it 
  }
}

add_action('manage_post_posts_custom_column','populate_post_custom_columns',10,2);

Hope it will be usefull.