Most new themes, and especially all Block Themes, offer a way to infinitely scroll posts: https://wordpress.org/themes/tags/full-site-editing/
Block Themes use the new Site Editor, meaning that how you can modify a theme is now almost limitless without even having to touch CSS: https://wordpress.org/documentation/article/site-editor/
There’s also a video tutorial if you prefer that style: https://learn.wordpress.org/tutorial/intro-to-the-site-editor-and-template-editor/
If you must use a Classic Theme instead, the Jetpack plugin offers a way to enable infinite scroll: https://jetpack.com/support/infinite-scroll/
Sorry none of what you posted has anything to do with the question i asked?
What you are looking for is perfectly feasible, but it depends very much on the data to be displayed and the theme. Your example is a WordPress and has a filter that was obviously written individually for the project and integrated into the theme.
You can try integrating one of the existing plugins into your project. However, whether it works depends heavily on your project.
Here, for example, is a plugin for filtering categories via AJAX: https://wordpress.org/plugins/category-ajax-filter/
Or here is one for WooCommerce products: https://wordpress.org/plugins/woocommerce-ajax-filters/
If you tell us what your site is based on and what content you want to filter, we may be able to give you further advice. However, you may also need to have this developed individually. You can get support for this, for example. here: https://jobs.wordpress.net/
Anonymous User
(@anonymized-23157725)
you can find load more, ajax filter or whatever you aim to do in your wordpress page on websites offering sample code snippets including codepen and enqueue these snippets to your wordpress site via funtions.php
