I've long felt that this was an obvious and good use of Emacs - as a central coordination point for the entirety of one's computational life, with everything manipulated programmatically from a single programming environment with both rich UI capabilities and a full-fledged programming language. No other project seems to understand the value of such a central point... but still, there are many ways Elisp could improve to make this kind of usage easier.
No. But I do use Emacs Lisp to automate certain tasks and then wrap them up in an Emacs interface -- like highlighting some JSON to submit to an API endpoint, or using ivy to select a Docker container to start or stop.
> You mentioned network connections - do you actually do scripting with Elisp's networking primitives?
Emacs provides an OOTB way to hit API endpoints in the form of 'request'. So it's not just the networking primitives, but the utilities built on those primitives that Emacs comes with.
> there are many ways Elisp could improve to make this kind of usage easier.
Emacs Lisp has had two major warts: speed, and the lack of lexical scoping and CL-like constructs. The latter is largely addressed. The former is being worked on with efforts like gccemacs.
Your answer: Learn Lisp!
Technically true even in spite of emacs, but if every engineer out there learns lisp to write better python wouldn't that be an interesting world.
This is also true for VS Code (with JavaScript instead of Emacs Lisp of course). VS Code is just a bit more organized on the surface, giving it significant advantages over emacs in that regard, but also a bit more closed in culture.