All category pages in grid

Should have added I would like only posts of the category selected to show.

Hello,

If you don’t have many categories, you can create View for each category, then modify category.php file to show relevant View for each category.

But it is time & effort consuming. If you want to make it works quickly without hassle, CVPro plugin at https://www.contentviewspro.com/ will help.
It has function to display posts on any page in any layout you want.
Here is document for this feature https://docs.contentviewspro.com/completely-replace-wordpress-layout-by-content-views-pro-layout/

Best regards,

I am using a search and filter plugin to help people navigate through the posts. It does not appear that with even the pro version I would be able to have them filtered. Is this correct?

With Pro version, you can display results of any plugin (as long as they use WordPress query functions) in Grid layout easily with some lines of code (like this).
Best regards,