Сервер Samba: Кто использовал все наше устройство хранения данных вчера?

The closest I think you can get is by using the -size parameter to find. Otherwise, you would need to have a report of usage from yesterday to compare the current state to.

big new files

You can use the find -size directive along wiht your -mtime to find these.

heavily grown directories

This will be impossible without historical data to compare with.