How to set “section categories”?

If you would like to add taxonomy other than default, you need to create another one by using register_taxonomy()
Because by default, only category and post_tag are created and associated to post.

Add the following code in functions.php

// 'post' is the post type name that you want to associate this new taxonomy to.
function q363839_create_new_tax() {
    $args = array(
    // please refer to the link above and add your settings here according to the need
    );
    register_taxonomy( 'section_category', 'post', $args );
}
add_action( 'init', 'q363839_create_new_tax' );

If in case you are creating taxonomy using plugin in.
Make sure you choose the following value to true so that it will appear in your custom post type eg. Artwork Admin Column

Show Admin Column - True

enter image description here

Edited: About the theme interference
I suddenly have an idea on how to solve the problem that is being created by the theme. You may try to

  1. search the code for register_taxonomy(), see what is the name of the taxonomies
  2. unregister it by unregister_taxonomy()
  3. create your taxonomy in CPT UI

OR

The best, you contact the theme author because the author for assistance knows it the best and will be the support for you.

Then you could be free from interference of the theme provided that you are sure that after removing the taxonomy from the theme will not break your templates.
If it break, then you just go to Screen Options to hide the default taxonomy and use your own one.

Related Posts:

  1. Custom Taxonomy – Tags Metabox is showing instead of Categories
  2. Why does my taxonomy have a category style div id?
  3. The Difference Between Categories and Tags and Taxonomies and Terms
  4. Advanced archive url structure (category, tag and date)
  5. Organizing The Custom Post Type with Taxonomies / Parent Posts
  6. How can I list all the categories under a Custom Post Type (taxonomy)?
  7. Glossary with Custom Post Type
  8. Custom-Taxonomy as categories: Remove “most-used” tab?
  9. Add filter to wp_list_categories and query what type of taxonomy-terms it use?
  10. Custom edit post column – category not showing
  11. How to search from specific post type with tags?
  12. Custom post type taxonomy template
  13. Categories and Tags not working!
  14. Display Posts of a Category in Alphabetical Order (Custom Post Type)
  15. Taxonomy structure of Sport site
  16. Is it possible to make tag archive page specific to Custom Post Type?
  17. Display Custom Category (taxonomy) Name in Custom Post Type
  18. get_categories() for only CPT
  19. custom taxonomy archive by year
  20. Search doesn’t find tags or categories in custom post types
  21. Querying Term Posts in Loop
  22. Can custom taxonomies items have attached properties?
  23. Weird problem happening with custom taxonmy when creating/updating posts
  24. Insert HTML inside link in a walker
  25. Set menu active state for custom posttype and category, given custom taxonomy term
  26. Posts from all the categories are being displayed instead of particular category
  27. Conditional Statement custom post type category
  28. Categories sorting
  29. Allow user to set custom order to a list of custom taxonomies?
  30. search also in taxonomy, tags and custom fields
  31. wp_list_categories() – current-cat class also inside posts?
  32. Listing tags from a custom post type
  33. Show a Category X’s custom post type on Category X archive page?
  34. Hide parent categories when clicked, and show it’s childs
  35. Limit amount of posts made within a custom taxonomy
  36. Filter CPT posts by one or more categories
  37. Getting categories of posts under a custom taxonomy
  38. How to edit this code to get the categories in achieve page?
  39. Hierarchy and access control for Custom Post Types (CPT)
  40. Best method to make posts searchable, sortable and filterable – custom field, tag or category?
  41. Cross reference custom post types
  42. I am trying to hide a custom post type category to logged in users with Pre_Get_Posts
  43. How can I show 1 featured post in a styled element, and the next few below differently styled
  44. Custom Post Type Category Link
  45. Custom Post type category pages template and loop
  46. Show all tags on custom post type
  47. Best way to specify “article type” in URL
  48. Tag page only display 10 posts
  49. in_category for custom post types
  50. Get parent category id from child category page for custom taxonomy
  51. How to add current custom taxonomy slug to body class
  52. Meta data (Tags and Categories) for Custom Posts not showing.
  53. List Posts By Custom Taxonomy
  54. How to Display Posts From Category Within a Custom Taxonomy?
  55. Disable custom taxonomy on admin bar
  56. portfolio custom type tags support
  57. How can I create an automatic drop down menu with my tags?
  58. Need help deciding on a taxonomy
  59. display custom taxonomies limited to custom post type?
  60. Listing all slugs?
  61. Get Posts by Category, Tag , and CPT Taxonomy
  62. Get child categories of custom taxonomy category?
  63. add custom tags for custom post type in wordpress
  64. Displaying One Custom Post Type’s Content On Single Post of Another Custom Post Type
  65. Custom post types category
  66. Get terms for a specfic post from multiple taxonomies in custom post type
  67. Custom post not appearing under custom taxonomy category
  68. Custom post type, taxonomy and admin bar
  69. how to organize my categories or should I do custom post types for some?
  70. Using get_terms() to list terms from one custom taxonomy AND from one specific built-in category
  71. How to divide Subcategories into pages of parent category wordpress
  72. Custom front-end form for adding post – Category problem
  73. How to show related posts of category on post within custom posttype
  74. get taxonomies from terms
  75. Tags being removed upon updates to related posts: ACF/Genesis/WP5.4.1
  76. CPT tags not showing when editing post
  77. Create custom post type categories
  78. Show Custom Post Type based on Category on Archive Page
  79. How to add independent “Tags” to Custom Post Type?
  80. How to manage a dynamic multi-level page hierearchy system?
  81. Categories manage
  82. Custom category taxonomy – archive page not showing up
  83. Help with Travel Guide Setup
  84. Add tags to a “pending” post before publishing
  85. Custom post type category archive URL redirects to home page
  86. Help with Multi Level Category Archive Page
  87. Display 2nd category, only once, as sub-heading, in the loop
  88. WordPress Custom Post Type and sort by Tags
  89. Get a list of categories ids
  90. Trying to create hierarchy between 3-4 custom post types
  91. Display a custom post type list by taxonomy term
  92. get tags from custom post type
  93. Return Custom Post Type Categories
  94. Remove slug from Custom Category Permalink + dual-category permalinks
  95. Highlight specific menu item when custom post is page
  96. Attaching multiple custom taxonomies to one CPT?
  97. Can WordPress show posts based on a button that the user clicked 2 pages back?
  98. How can I show second most recent post in sidebar, if most recent post is open in the browser?
  99. Is it possible for post and custom post type to share a category base slug?
  100. How to add categories to a custom post type using wp_insert_post($new_post);