How to display the description of a custom post type in the dashboard?

this answer is for showing the description in the menu. if you want show it somewhere else, you should create a new question.

I often try to propose solutions that don’t use javascript if not necessary. but for this customisation, there is not practical hooks to do that then I think it will be no very reliable to use output buffering.

in the following code, put the slug of the CPT, the URL of the javascript file and replace MY_PLUGIN by the slug of your plugin to limit interference with other plugins.

code to put in menu.js

"use strict";


document.addEventListener("DOMContentLoaded", e => {
    
    const menu_entry = document.querySelector(`#menu-posts-${MY_PLUGIN["cpt_slug"]} a.wp-has-submenu`);
    
    const description = document.createElement("div");
    description["textContent"] = MY_PLUGIN["description"];
    description["classList"].add("cpt_description");
    
    menu_entry.insertAdjacentElement("afterend", description);
    
    
});

loading of the javascript code

add_action("adminmenu", function () {
    
    wp_enqueue_script(
          "MY_PLUGIN/menu"
        , "menu.js" // URL of the file
        , []
        , 123 // version of the file menu.js
    );
    
    
    $cpt_slug = "tache_et_procedure"; // CPT slug to correct here
    
    $obj = get_post_type_object($cpt_slug); 
    
    wp_localize_script(
          "MY_PLUGIN/menu"
        , "MY_PLUGIN"
        , [
            "cpt_slug" => $cpt_slug,
            "description" => $obj->description,
        ]
    );
    
    
});