refactor!: restructure Doom core

BREAKING CHANGE: This restructures Doom's core in an effort to slim it
down and partially mirror architectural changes coming in v3. This is
part 2 of 3 commits (part 1 being 1590434), done to facilitate a change
in part 3 that will introduce a new `doom!` syntax for pulling
third-party module libraries from remote sources (similar to `package!`
statements). I am backporting this from V3 so I can move our modules out
into separate repos sooner than later, so development on modules can
continue separately without interfering with v3's roll out.

Though this is labeled a breaking change, it shouldn't affect most users
except those few tinkering directly with Doom's internals.

Ref: 15904349cf

lisp/cli/doctor.el

@@ -328,7 +328,7 @@ in."
                               (packages-file (doom-module-expand-path (cons group name) doom-module-packages-file)))
                           (when packages-file
                             (cl-loop with doom-output-indent = 6
-                                     for name in (with-doom-context 'packages
+                                     for name in (with-doom-context 'package
                                                    (let* (doom-packages
                                                           doom-disabled-packages)
                                                      (load packages-file 'noerror 'nomessage)