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Saving yields a psd which indeed requires PS. Whether project lives "inside" app or not it's still bound to it by format, and separate from your source.PSD files can be read by other applications. Not perfectly, but can. Many other proprietary formats have been reversed or opened to the point that other applications can read or edit them. And then there's a whole set of formats that aren't tied to any application per se. No app owns JPG, PNG, WAV or CSV.
> whether edit-in-place is accomplished through system file manager or back and forth across apps through piping and callbacks is just an implementation and workflow detail.
It's not an implementation detail. The "back and forth across apps through piping and callbacks" is under control of the app developers, and the extent to which it works depends on the contractual deals they sign between each other. A file system is an universal intermediary layer owned by no one, which maximizes interoperability and doesn't require the user to maintain or be aware of relationships between app vendors.
(Or, look at it from a software design point of view. If you were presented with large and potentially dynamic network of components exchanging data through APIs, you might actually come up with a file system equivalent as a way of separating concerns and maximizing composability.)
> the difference between On my device and iCloud isn't clear or something
That would be an important difference to have. Basically, "I'm on a train and Internet is spotty, or my ISP has an outage, will I be able to open and work on this file or not?" is a question for which the answer is kind of critical. The Internet is not electricity, it's not always available.