Visiting a console submenu page does not expand its parent menu item

You can use the parent_file hook to ensure the TDLRM menu is expanded when viewing the “Store users” or “Categories” page.

add_filter( 'parent_file', 'wpse_398962_parent_file' );
function wpse_398962_parent_file( $parent_file ) {
    global $submenu_file, $typenow;

    // 1: This is for highlighting the TDLRM » "Store users" submenu.
    if ( 'users.php' === $parent_file && ! $submenu_file &&
        isset( $_GET['role'] ) && 'tdlrm_store_user' === $_GET['role']
    ) {
        $typenow = true; // this trick ensures the parent file/slug is TDLRM

        // This highlights the "Store users" submenu.
        // Make sure it matches the slug you passed to add_submenu_page().
        $submenu_file="users.php?role=tdlrm_store_user";

        return 'TDLRM';
    }

    // 2: This is for highlighting the TDLRM » Categories submenu.
    // Make sure the value matches the slug you passed to add_submenu_page().
    if ( 'edit-tags.php?taxonomy=store-category&post_type=tdlrm_store_item' === $submenu_file ) {
        return 'TDLRM';
    }

    return $parent_file;
}

Notes:

1. There is a trick above which is used for expanding the TDLRM menu, but only when viewing the “Store users” page.

   And what the trick does is, it prevents get_admin_page_parent() from changing the parent file ($parent_file) to users.php.

2. WordPress escapes special characters like ampersands (so & becomes &) in the menu/submenu slug, hence your “Categories” submenu needs to use a valid/properly-escaped slug in order for the submenu to be highlighted when viewing the TDLRM » Categories page.

   // Note below I used & instead of just &
   add_submenu_page('TDLRM', 'category_redirect', 'Categories', 'administrator',
       'edit-tags.php?taxonomy=store-category&post_type=tdlrm_store_item');
   

And actually, instead of having to use the tdlrmm__menu_edit() function, you could simply set the show_in_menu arg to My-menu (the menu slug), and then “Teasers” ( or whatever is the (plural) label of your post type ) would appear as a submenu under your “My-menu” menu.

However, be sure to read the note here which says, “this item will become the first submenu item, and replace the location of the top-level link. If this isn’t desired, the plugin that creates the menu page needs to set the add_action priority for admin_menu to 9 or lower“.