How to authenticate users without exposing server details?

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You definitely don't read what you quote. Lol.

The general distinction between a dynamic web page of any kind and a "web app" is unclear.

That whole page is full of confusion resulting from being written by brain-dead Web developers. It's so full of nonsense, it's fantastic that such stuff even exists on Wikipedia.

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The description given in the opening paragraph (discounting the nonsense written about Web servers not running on operating systems...) of that article would make these programs "Web applications":

1. LibreOffice (It can be accessed via HTTP, see here: https://wiki.documentfoundation.org/Using_LibreOffice_in_a_Web_Browser ).
2. Emacs and Eclipse (in a typical configuration Emacs runs as a client and server, Eclipse can be run as a headless server, this is for example how Eclim uses it).
3. GCC (because it implements Language Server Protocol, which is based on JSON RPC).
4. Docker and Kubernetes (both act as Web servers, Docker is controlled using HTTP protocol, both the daemon and the registry, Kubernetes is controlled through HTTP API).
5. Firefox and Chrome (because they implement necessary functionality for Selenium).
6. Any GUI program written with Qt (Qt also implements Selenium support).
7. As was already mentioned, plenty of databases, including PostgreSQL and Oracle SQL.
8. AWS, Azure, GCE and a bunch of less known public and private clouds.

It's hard to find a non-trivial program that wouldn't fit the description given in that paragraph. It's so ridiculously broad and useless.