Are you able to send me a live link/URL to the current search page so I can take a look?

That seems pretty straight forward. The search bar on top on the results and the sidebar form will need to be combined in to one single form in the sidebar.

You may need to use Relevanssi (a free plugin) to enhance what data that search bar (text box) can search:

https://searchandfilter.com/documentation/3rd-party/relevanssi/

The sidebar form appears to contain three custom taxonomies:

Contracts Type
Member Type
Regions

If they are not set up that way, they will need to be (as separate custom taxonomies). You should be able to add one or more ‘Taxonomy’ fields to the Form UI, then in each field settings section, you can select the specific taxonomy you need to filter by. For example:

https://www.screencast.com/t/ciqj5LfW

Are the members a custom post type, or did the site designer add them as posts?

How are you going to make the grid? Are you going to use a PHP template, or a Page Builder? If you are going to use a Page Builder, I would suggest looking at Elementor Pro. We have a integration for that:

https://searchandfilter.com/documentation/3rd-party/elementor/ (there is an extension plugin at the top of that guide that you can download)

One advantage of using page builders like Elementor Pro, is that you can use it with pretty much any theme (I can use it with their free Hello theme for example). No need to buy a premium theme.

OK. Well, that being the case, make a form using the Post Type Archive display results method and set it to search the Members Post Type. It should work. Set it at first with Ajax OFF to test.

OK. I will wait to hear from you.