Hi,
1. The number of posts per page in this case depends on the Elementor widget configuration as well. Make sure to change that in the Elementor Posts widget settings. That number will be automatically passed to Ajax Search Pro as well.
Do you happen to use any fancy Elementor addon, which may change the appearance or functionality of the posts widget? Those could very well cause a conflict with the pagination.
2. May I take a look at the code directly? I tried to log-in with the details, but the server does not allow accessing the wp-admin area. Can you please also add temporary FTP details, so I can debug this directly? Thank you!