php.ini does not belong in the phplist directory. It’s usually located somewhere in /etc or /usr/local/etc, depending on your OS. If you’re running Apache, you can try to trick it with .htaccess (create it under /mnt/webm/c1/93/53299493/htdocs/phplist/), which should contain the line
php_value open_basedir “/mnt/webm/c1/93/53299493/htdocs/phplist/”
If you are not running Apache, you can try renaming the php.ini as .user.ini (yes, it’s a dot before user). Some (but not all) installations of PHP (starting with 5.3.0) pick it up. The service provider, however, may have changed that behaviour. I have limited experience with virtual hosts so I cannot really comment on how things are set up at Strato, and my knowledge of German is limited to ‘ich habe Sauerkraut in meiner Lederhosen’ so I cannot really decipher the relevant portions of their website that well. Anyhow, if you can make PHP pick up that value, it should be smooth sailing with 7.0.