Web directories have been disused several years ago and all the software I knew (such as eSyndiCat) did not seem very up to date.
Does anyone know if there are modern CMSs (in Php) to create web directories?
Have a look at Drupal, a modern CMS, and written in PHP. It can be used to build virtually any kind of websites, so for sure also for "web directories".
These days there are typically 3 releases of it being used: