I have a suspicion, which I have never verified, that the things that make emacs great are basically the things that made Lisp Machines great back when those were a thing - that emacs is best viewed as a Lisp Machine embedded in a modern operating system.
I never used a real Lisp Machine, but I'd love if someone who did can confirm this.
EXWM or StumpWM+Emacs, since the window managing bits are pretty small compared to other tasks (manipulating text of various sorts) that one would use Emacs for.
Lisp machines were indeed a whole other level. Everything integrated with everything. We're getting closer though with emacs in stumpwm and eaf. There's plenty of room for scope in extending stumpwm.
GNU Emacs is just an example of extensible Lisp software running on top of an operating system. Lisp software, which sometimes provide integrated IDE features. Other examples: Autocad and some other CAD systems, OpusModus ( https://opusmodus.com ), ... There are also other Emacs variants with a similar idea. The original Emacs variants which introduced the idea of a Lisp written extensible Editor were EINE/ZWEI on the Lisp Machine (written in Lisp Machine Lisp) and Multics Emacs (written in Maclisp for the Multics OS). There were and are a multitude of Lisp systems with integrated editor / IDE written in itself - the most elaborate examples are the commercial Lisp IDEs coming with Allegro CL and LispWorks.
GNU Emacs provides an application programming environment based on an editor-like paradigm (windows, text buffers, programmable modes, ...) and integration of external tools. This toolkit has then been used to implement its own IDE.
Most people haven't seen extensible Lisp-based software. For another example look at Smalltalk-based software, which also comes with its integrated development environment - which is largely written in Smalltalk itself.
Actual "Lisp Machines" differ from GNU Emacs in many ways: They were actually real computers: real hardware - sometimes even specialized hardware like the 36bit / 40bit tagged memory of Symbolics Lisp Machines - the machine used specialized memory cards for that. These systems had a Lisp Operating System covering all layers of the operating system and its applications. They provided an editor (often a variant of Emacs) as one application, but the user interface was mostly not based on text buffers in windows with modes. Historically most Lisp Machine software was written in rich Lisp dialects, often making heavy use of OOP.
There are a bunch of ways GNU Emacs talks to the surrounding operating system: direct calls to the OS, running external programs, connecting to external applications over the network via some protocol (an example would be the SLIME IDE for Common Lisp, which connects GNU Emacs to an external Lisp via a network connection), ... Some GNU Emacs applications can be largely implemented with internal functionality and occasional calls to the OS or other applications.
On a Lisp Machine (the ones which existed so far) everything runs inside a shared memory heap where most stuff is implemented in Lisp: process scheduler, network stacks, disk drivers, file system, printer drivers, graphics, user interface, other programming language compilers, ...
Summary: GNU Emacs shares a bunch of features with other extensible Lisp software, including the software side of Lisp Machines. GNU Emacs does not work or looks like actual historical Lisp Machine systems (MIT Lisp OS, Symbolics Genera, LMI / TI Lisp OS, Xerox Interlisp-D / Medley, ...) .
I never used a real Lisp Machine, but I'd love if someone who did can confirm this.