Trying to create a url rewrite for a list/detail page

I'm trying to create a url rewrite rule for the detail page in a list/detail scenario, similar to what I use for blog.

The list page is /case-studies/case_studies.php

The detail page is /case-studies/case_studies_detail.php

With the php slug, a typical url looks like this: https://my-site.co.uk/case-studies/case_studies_detail.php?s=my-case-study-title

I'm trying to rewrite this so that it appears in the browser as https://my-site.co.uk/case-studies/my-case-study-title

My .htaccess file contains these lines:

RewriteEngine On

# Exclude the Perch CMS directory from any rewrites
RewriteRule ^admin - [L] 

# Rewrite for case studies list/detail page
RewriteRule ^case-studies/([a-zA-Z0-9-/]+)$ /case-studies/case_studies_detail.php?s=$1 [L]

# Rewrite for SEO friendly url
RewriteRule ^blog/([a-zA-Z0-9-/]+)$ /blog/post.php?s=$1 [L]
RewriteRule ^preview/$ /preview/post.php?s=$1 [L]

The blog rewrite works fine, the case-studies rewrite doesn't. It just doesn't seem to take effect, I still see the php slug (the page navigations from the list page to the detail page work fine).

The live site is here: https://downing-ip.uk/case-studies/case_studies.php

I'd appreciate any insights... Thanks