Sorry that you encountered this, @mizaistom and @leichim.
As a workaround for now, please could you try installing Local via yum or Fedora’s Software Installer as above, then also installing the missing dependency like this?
sudo yum install libxcrypt-compat
Restart Local, and you should find that MySQL runs when you create and start a new site. I tested this under Fedora 39 and all is then well for me:
(The underlying issue is that the vendor-supplied version of MySQL that Local defaults to (8.0.16) is linked against a dynamic library (libcrypt.so.1) that was removed in newer versions of Linux/Fedora. We’ll look at upgrading to a newer version of MySQL (8.2.x) that links to later libcrypt versions, but I don’t yet have a timeline for this work. I hope the workaround helps you for the time being.)