How to teach the site to add arguments to the URL when fetching in an AJAX filter?

Question

WordPress

Yes, a future catalog project. It has an AJAX filter https://catalog.mediagroup.space/explore/
When selecting search arguments, nothing is added to the URL, so the user cannot share a search link with someone.
The question is, how can this be organized?
CMS wordpress. The catalog software is the WP Job Manager plugin.
Thank you.

Answer 1

For each form change, you run a function that runs through the form, collects information about the field values ​​and places it in an array or string, and then in a hash.
Your form elements are not native, so the code will not work 100%, but the direction is given to you:

window.location.hash=jQuery("#search-form > div.search-filters.type-place > form").serialize()