Ajax filter with loadmore button

You could possibly look at doing this the same way that WP Job Manager does:
https://github.com/Automattic/WP-Job-Manager/blob/master/assets/js/ajax-filters.js

This is done by triggering a handler to make the query defining what “page” the query should run against. I would recommend using that as an example to build off of, as it works with both filters applied and none being applied.

ALSO ALWAYS ALWAYS ALWAYS SANITIZE USER DATA
Anywhere you’re using $_POST $_GET $_REQUEST etc you should always sanitize the data before using it anywhere. Best to get in the habit of it or bad things could eventually happen.
https://developer.wordpress.org/themes/theme-security/data-sanitization-escaping/