Just keep a desktop or get a NAS or something.
Incidentally, I do believe Calibre runs on the Raspberry Pi 4. It’s ARM-based and significantly less powerful than even a 2-3 generations old iPad. However, barring packages incompatible with ARM, it does offer the full Linux experience so you can install Calibre on it. Meanwhile, iOS is restricted by design.
By the way, the iOS Files app couldn’t handle my Paperwhite 3 which has around 2000+ books. It even managed to make my Kindle crash somehow.
The Files app uses an abstraction layer or something and doesn’t actually provide direct file system access. I’ve had it crash on me a few times during normal use, no external storage connected. I wouldn’t trust it not to corrupt my data.
Also note, I do believe the KFX output plugin requires Kindle Previewer. Even if someone does write an ebook conversion app for the iPad, converting to KFX likely won’t be an option.