Simple way to add to a post grid

can you try to explain it a bit more precise: “I could add a conditional badge to the display grid.”

Or try to give us a mockup or sketch. – What do you mean by display mechanism?

is it like this ? ( but with different images , or icons ) :

no i had to see your example page – to see how to differ between the posts.

and not to use category – you can use post tags for it.
To have the post tag on single post as body class you can use this in child-theme functions.php:

function add_tags_to_body_class( $classes ) {
if( (is_single()) && $tags = get_the_tags(get_queried_object_id())){
    foreach( $tags as $tag ) {
        $classes[] = 'tag-' . strtolower($tag->name);
    }
}
return $classes;
}
add_filter( 'body_class', 'add_tags_to_body_class' );

for blog – you can forward these classes as classes on the article.slide-entry
for that you had to edit as Nikko mentioned the postslider.php:
( and the link from Nikko to add-elements-to-alb shows you how to have a child-theme alb element.)

just before that line 900 ( see codeblock of Nikko ) insert:
( the strtolower brings all tags to lowercase – so a tag : Eating will end in a class: tag-eating )

$posttags = get_the_tags($the_id);
foreach($posttags as $posttag)
{  
	$post_class .= 'tag-' . strtolower($posttag->name) . ' ';
}

then you can set on your posts the tags : badge1, badge2, badge3 or commerce-member etc
you will have on article then the class: tag-commerce-member or tag-badge1 etc.

now you can differ between those entries in f.e a grid blog.
If you decide to use that badge1, badge2, badge3 nomenklatura for your post-tags :
( the image names do not need to be synchronized with that tags )

.avia-content-slider, 
.avia-content-slider-inner, 
a.slide-image {
  overflow: visible !important
}

.slide-entry[class*='tag-badge'] a.slide-image:after {
  content: "";
  width: 50px;
  height: 50px;
  position: absolute;
  top: -10px;
  right: -10px;
  background-repeat: no-repeat;
  background-size: contain;
  box-shadow: 0px 0px 10px -2px #000;
  z-index: 301
}

.slide-entry.tag-badge1 a.slide-image:after {
  background-image: url(/wp-content/uploads/badge1.jpg) ; 
}

.slide-entry.tag-badge2 a.slide-image:after {
  background-image: url(/wp-content/uploads/badge2.png) ; 
}

.slide-entry.tag-badge3 a.slide-image:after {
  background-image: url(/wp-content/uploads/badge3.jpg) ; 
}
/**** etc. ***/

see f.e.: https://enfold.webers-webdesign.de/blog/

for those who are interesed in : forwarding the category of posts , taxonomy of portfolio-entries and tags on both as class to the body in single posts:

function add_tags_to_body_class( $classes ) {
global $post;	
	if( is_single() && ( $posttags = get_the_tags($post->ID))){
	    foreach( $posttags as $posttag ) {
	        $classes[] = 'tag-' . strtolower($posttag->name);
	    }
	}
	if(is_singular('post') &&  ($postcats = get_the_category($post->ID))){
	    foreach( $postcats as $postcat ) {
	      $classes[] =  'cat-' . strtolower($postcat->category_nicename);
	    }
	}
	if(is_singular('portfolio') && ($postterms = get_the_terms($post->ID, 'portfolio_entries'))){
	    foreach( $postterms as $postterm ) {
	      $classes[] =  'term-' . strtolower($postterm->slug);
	    }
	}	
	return $classes;
}
add_filter( 'body_class', 'add_tags_to_body_class' );

and having those classes on the article.slide-entry in f.e. blog grid or masonry see postslider.php code on https://pastebin.com/F9KPRkxQ
( changed lines 902ff )
You will then have the possibility to set different appearance of the postings within the blog based on the source using the selectors.

So the ulterior motive is that the provenance (category, keywords, taxonomy) is passed on when these posts are listed on a blog; and that the individual posts themselves can also be styled according to their belongings.

do you need any additional help?