If you're not using neovim you're really missing out right now IMO. It's a renaissance for a hackable text editor because it uses a sensible modern programming language (Lua) rather than vimscript (yikes) or elisp (eh).
Having worked with Lua and Elisp extensively, they have very different pros/cons profiles. In my experience, Lua is great as a scripting language - tiny, speedy, and completely dynamic. For "programming in the large(r)," Lua is just a little better than early JavaScript (i.e., tragic). The purity of the design - tables, metatables, closures, coroutines, and that's it - necessitates reinvention of tens of wheels (either in Lua or in the host app) when your codebase grows and complexity increases. Elisp provides two orders of magnitude more "bells and whistles" than Lua out of the box. Additionally, while Lua's primitives are extremely powerful, they are all strictly run-time constructs. Elisp has macros, so many abstractions can be (and are) shifted to compile time.
I use Awesome WM. It's essentially an "Emacs of Window Managers," and the codebase is very well written, with a small C core and everything else implemented in Lua. It's even very well documented. Yet, writing a nontrivial program (call it an "applet" or something) for Awesome is a nightmare compared to doing the same in Emacs.
LuaJIT is an excellent runtime, and Lua is a great IR, but writing it by hand for anything that's not strictly scripting within a previously established framework is challenging. It's to the point where I'm using Haxe to produce Lua for my Awesome scripts. I know a few people who use Haxe to script NeoVim, too. Really, having to reinvent inheritance and method resolution order every time you start writing Lua in a new project gets old fast.
I genuinely like Lua as a language - the same way I like Tcl, Scheme, and Io. They are all beautiful and powerful and perform very well in some scenarios. Elisp is ugly in comparison, but it's way more practical for medium-sized codebases. Being tied to Emacs is a considerable downside which limits its applicability, but focusing on language features alone, larger codebases are more practical to write in Elisp than in Lua. Plus, there's an escape hatch - Common Lisp or Clojure, pick your poison - for cases where Elisp actually doesn't cut it. There's no such easy way out for Lua.
You may be missing the point of Elisp. Elisp isn't an "extension language". It's the language Emacs is built with. When you run Emacs you're actually running a Lisp interpreter with a load of text editing features pre-loaded. When you eval some Lisp you're modifying the runtime, essentially live patching your editor in real time. So really any comparisons with Elisp are irrelevant unless you can do what it can do. Common Lisp and Scheme (Guile) are real contenders but the challenge is not giving up the enormous amount of useful code that is already written in Elisp.
That's not a JIT. It uses `libgccjit` (IIRC the name), but the native code is produced ahead-of-time. JITs compile using info available on runtime, and native-comp doesn't do that. LuaJIT, by contrast, is a "real" JIT. Still, native-comp does speed things up considerably.
I'm a big lisp fan. I know about all of this, I used emacs for maybe a decade, and I still don't like elisp. I love the hackability of Emacs, but it's OK to dislike the language itself. Disliking semantic choices of the language doesn't mean I'm missing the point either!
And on "it's not just an extensibility language": in my experience this doesn't matter. I get that "well the editor itself is half written in elisp" and so vaguely that is superior, but it is only so in an academic sense.
Expose the primitives for the editor in some API in _any_ langauge and you can basically achieve the same thing anyway, so pick a language that doesn't make me want to poke my eyeballs out with a hot skewer.
I think if you're just talking about writing extensions/packages (like magit) then the difference is not as big. But for using Emacs it makes a big difference. I can just start hacking on package code by redefining functions etc. and using/testing them straight away. The power of Emacs is not about being able to write extensions (most editors can do that), it's about being able to write tiny little bits of code to change your editing experience as you go. There are specific things in Elisp that make it good for this, like dynamically scoped variables. Writing extensions for other editors is always a "thing", a project. Writing Elisp to change how Emacs works is just using Emacs.
I will concede that you are probably a very different kind of Emacs user than I, since I pretty much exclusively used Elisp to set up and tune my editor to my liking as a totally independent act from actually using my editor to write programs.
For me, even when working on something besides my editor configuration, having access to the parts of the “editor primitives” makes for a lot of powerful one-off editing tools. It was relatively easy, for example, for me to us lsp features to get a list of undefined JS variables in the current scope and add them to the function argument list. And, since lsp and the other bits I put together are all in elisp, I could use jump-to-definition to quickly find the itnernals I need to make the change.
What you're describing is a feature of the system as a whole. You can have the same workflow with any dynamic, reflective environment. All Smalltalks give you the same ability to "jump to definition" of anything, turtles all the way down, and fiddle with those definitions. You could have the same ability in a system written in Lua - you just generally don't, because it requires designing the system as a whole specifically to allow it.
I use Awesome WM. It's essentially an "Emacs of Window Managers," and the codebase is very well written, with a small C core and everything else implemented in Lua. It's even very well documented. Yet, writing a nontrivial program (call it an "applet" or something) for Awesome is a nightmare compared to doing the same in Emacs.
LuaJIT is an excellent runtime, and Lua is a great IR, but writing it by hand for anything that's not strictly scripting within a previously established framework is challenging. It's to the point where I'm using Haxe to produce Lua for my Awesome scripts. I know a few people who use Haxe to script NeoVim, too. Really, having to reinvent inheritance and method resolution order every time you start writing Lua in a new project gets old fast.
I genuinely like Lua as a language - the same way I like Tcl, Scheme, and Io. They are all beautiful and powerful and perform very well in some scenarios. Elisp is ugly in comparison, but it's way more practical for medium-sized codebases. Being tied to Emacs is a considerable downside which limits its applicability, but focusing on language features alone, larger codebases are more practical to write in Elisp than in Lua. Plus, there's an escape hatch - Common Lisp or Clojure, pick your poison - for cases where Elisp actually doesn't cut it. There's no such easy way out for Lua.