Is there a "windirstat"/"Disk Inventory X" type iOS app? (ie app for visualizing hard drive usage on iOS)
Your only option is to make a backup of the iOS device on a Mac/PC, then use a third party tool to copy the files into the filesystem as regular files.

From there you can run Disk Inventory X or any similar tool.

Beware that iOS uses compression and doesn't necessarily store all of your files on the local device (photos and music in particular could be in the cloud), so this will not give you an accurate measurement. But it will be as close as you can get.