Render Modula Plugin Shortcode On Ajax Request

I can only comment on this on a general level as I’m not familiar with the plugin you’re using. (This might also not be the best place to ask this kind of plugin related questions as 3rd party plugins are currently considered off-topic here on WPSE.)

Majority of this kind of plugins I’ve encountered have some kind of javascript (or jQuery), which is executed on page load, which setup the layout, enable lightboxes and other features. After the scripts have run, they are done and don’t care about what happens to the DOM or html afterwards. This means that, if you add new html to the page via Ajax, you need to find a way to fire those same setup scripts again yourself.

$.ajax({
    success: function (data) {
        // add html to the DOM
        $('.target-div').html(data);

        // the basic idea..
        some_vendor_function_to_init_gallery(
            $('.target-div')
        );
    },
});

If these setup scripts are globally available depends on the plugin you’re using. You need to either dig into the plugin’s source code, browse its documentation, and/or contact the plugin author. If the setup script is not in the global scope, then you’re probably out of luck.