Someone linked the Plug docs elsewhere in this subthread, those show you how you can quickly launch a web server from a single file, including one with WebSocket capability.
In my opinion Elixir scripts punch way above their weight. It's trivial to pull in the same dependencies as you would in a full project and you can easily keep a set of five or ten template scripts just laying around and copy those when you want a quick start with some boilerplate for a set of dependencies that often comes in handy. You could do something similar with mix plugins but it requires a bit more effort.
Side-note: considering you like Prolog, how come you are not writing Erlang instead of Elixir?
I actually like Erlang, but I personally feel it has a lot of rough edges. I'd probably spend a lot of time polishing them to the point where I'd just reinvent Elixir, so I prefer Elixir for that reason alone.
The other reason I wouldn't use Erlang is that Elixir has a much more vibrant & active community. A lot of the Erlang libraries (as of a few years ago when I last looked) were quite old & there wasn't a lot of active development being doing on them. I like being able to track down answers to questions & documentation that is more current. And of course there are more likely to be off the shelf Elixir libraries available for download, too.
It's harder to teach to juniors with a background in stuff like JavaScript and Python. While it has a rather nice elegance and simplicity to it Erlang is a bit more demanding from a business and organisational perspective.
A clever intern with a rather shallow two year 'bootcamp' education and no work experience picks up Elixir and Phoenix in a couple of months. People with background in enterprise algolians like Java and C# can also get productive in Elixir kind of fast since it allows similar patterns.
In my experience Lisp-like languages prepare well for Erlang, and that's a very rare background where I live.
Where do you live if you do not mind asking? Europe? Western Europe, Eastern Europe?