Removing data without formatting the iPhone
Assuming you're not talking about a very old iPhone (i.e. iPhone 5 or older), then every file created by any app is actually encrypted on disk. The plain text content is not stored on disk at any time.

In addition, every file is encrypted with a unique key - i.e. there's a seperate key for each file. The key for the file is stored alongside the encrypted file contents, but encrypted with a so called "class key" (depending on the settings in the app). This is the foundation of the key hierarchy in Apple's "Data Protection" scheme.

When you delete an app manually, all the files stored locally by that app are deleted. This deletion of each individual file is actually done by simply deleting the per-file key. This makes it possible to delete even very large files quickly and securely at the same time.