How can I permanently delete files I manually deleted?

Not entirely sure of your situation, or whst part of ‘permanently delete” you’re asking about…

If the videos are in iCloud, deleting them from one place deletes them everywhere.

For whether the data can be recovered, deleting files on flash storage automatically erases that storage.

And depending on which app you’re using here, there can be a deleted media album or folder around.

If you’re using Photos, see: Delete photos on your iPhone, iPad, and iPod touch - Apple Support