如何使用nginx别名为php-fpm设置正确的root？

I would like to change the html/php root for every user in a separate directory like:

abc12345 has its root-directory for html/php at: /home/abc12345/html/

This works already for non-php-files with following configuration:

     location ^~ /abc12345 {

            alias /home/abc12345/html;
            index index.php;

            location ~ \.php$ {
                    #include fastcgi_params;
                    fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;

                    fastcgi_param PATH_INFO $fastcgi_path_info;
                    fastcgi_intercept_errors on; 

                    fastcgi_param HTTPS on; 

                    fastcgi_split_path_info ^(.+?\.php)(/.*)$;

                    try_files $fastcgi_script_name =404;

                    set $path_info $fastcgi_path_info;
                    fastcgi_param PATH_INFO $path_info;

                    fastcgi_index index.php;
                    include fastcgi.conf;

                    fastcgi_pass unix:/var/run/php/php7.3-fpm.sock;
                    #try_files $uri =404;
            }


     }

As soon as I pass an php-file this does not work, cause the SCRIPT_FILENAME will try to search under /home/abc12345/html/abc12345/test.php

Even if I try

                    fastcgi_param SCRIPT_FILENAME $request_filename;

the directory would be /home/abc12345/html/abc12345/test.php

What is the correct configuration for fastcgi_param to escape the ../html/abc12345/..?