Drupal in sub directory, still not clear
Apache can handle this. You can leave the Drupal code where it is.

Have a look at the Apache documentation for Mapping URLs to Filesystem Locations. In particular, the differences between DocumentRoot and Alias.

In the absence of any other information, Apache looks for files/scripts in the document root. For a Drupal site located at https://www.myorganization.it/, it's enough to point DocumentRoot at the web directory. Apache will find index.php there.

But myproject isn't a directory in the filesystem. So you need to explicitly tell Apache about it, that any URL starting /myproject refers to the web directory. You can do that with the Alias directive:

Alias "/myproject" "/var/www/MY_ORGANIZATION/MY_PROJECT/current/web"

You'll also want to point DocumentRoot somewhere else to stop Drupal being visible at the root too (an empty directory will do).