[eglot] Add support for eglot lsp client in emacs

- Update README
- Add eglot-specifics to cc, rs, py, hs
  removing unused lsp-mode packages when eglot is active
- Add eglot-specific bindings
- Add doctor warnings for debugger +lsp and +peek
- Add eglot-backed lookup-handlers
- Add flycheck checker using eglot for :checkers
  syntax users (using flycheck/flycheck#1676 and
  flycheck/flycheck#1592 discussion).
  This implementation is based on @marsam code, and uses recent
  Flycheck development in order to make the code smaller and
  easier to maintain.

modules/tools/lsp/README.org

@@ -56,10 +56,16 @@ As of this writing, this is the state of LSP support in Doom Emacs:
 ** Module Flags
 + =+peek= Use =lsp-ui-peek= when looking up definitions and references with
   functionality from the =:tools lookup= module.
++ =+eglot= Use [[https://elpa.gnu.org/packages/eglot.html][Eglot]] instead of [[https://github.com/emacs-lsp/lsp-mode][LSP-mode]] to implement the LSP client in
+  Emacs.
 
 ** Plugins
 + [[https://github.com/emacs-lsp/lsp-mode][lsp-mode]]
 + [[https://github.com/emacs-lsp/lsp-ui][lsp-ui]]
++ [[https://github.com/emacs-lsp/lsp-ivy][lsp-ivy]]
++ [[https://github.com/emacs-lsp/helm-lsp][helm-lsp]]
++ [[https://github.com/joaotavora/eglot][eglot]]
+
 ** Hacks
 + ~lsp-mode~ has been modified not to automatically install missing LSP servers.
   This is done to adhere to our "Your system, your rules" mantra, which insist
@@ -75,15 +81,37 @@ You'll find a table that lists available language servers and how to install
 them [[https://github.com/emacs-lsp/lsp-mode#supported-languages][in the lsp-mode project README]]. The documentation of the module for your
 targeted language will contain brief instructions as well.
 
+For eglot users, you can see the list of [[https://github.com/joaotavora/eglot/blob/master/README.md#connecting-to-a-server][default servers supported in the README]].
+There is also instructions to add another server easily.
+
 * TODO Features
 ** LSP-powered project search
-When =:completion ivy= or =:completion helm= is active, LSP is used to search a
-symbol indexed by the LSP server :
+Without the =+eglot= flag, and when =:completion ivy= or =:completion helm= is
+active, LSP is used to search a symbol indexed by the LSP server :
 | Keybind   | Description                         |
 |-----------+-------------------------------------|
 | =SPC c j= | Jump to symbol in current workspace |
 | =SPC c J= | Jump to symbol in any workspace     |
+** Differences between eglot and lsp-mode
+Entering the debate about which one to use would be useless. Doom provides an
+easy way to switch out lsp client implementations so you can test for yourself
+which one you prefer.
+
+Mainly, from a code point of view, lsp-mode has a lot of custom code for UI
+(=lsp-ui-peek=, =lsp-ui-sideline=, ...), while eglot is more barebones with a
+closer integration with "more basic" emacs packages (=eldoc=, =xref=, ...).
 
 * TODO Configuration
 
 * TODO Troubleshooting
+** My language server is not found
+Check the entry in the [[../../../docs/faq.org][FAQ]] about "Doom can't find my executables/doesn't inherit
+the correct ~PATH~"
+** LSP/Eglot is not started automatically in my buffer
+Make sure that you added the =+lsp= flag to the language you're using too in
+your init.el :
+#+BEGIN_SRC diff
+:lang
+-python
++(python +lsp)
+#+END_SRC