Most of the mobile encryption schemes are using file system encryption, not block encryption, i.e. the metadata is not encrypted other than directory and filenames. There's a range of opinions to what degree the unencrypted file metadata: file sizes, dates & time, relative locations in the directory tree, can be used to infer... what? some kind of pattern that suggests the owner is using or once used an app banned in the country they're entering?

We know metadata between e.g. browser and server, two callers, message sender and recipient, can reveal quite a lot. But it's quite a bit more limited with file metadata, but to what degree is this a problem?