feat(lsp)!: remove client-server handlers from vim.lsp.handlers

- Partition the handlers in vim.lsp.handlers as:
  - client to server response handlers (RCS)
  - server to client request handlers (RSC)
  - server to client notification handlers (NSC)

  Note use string indexes instead of protocol.methods for improved
  typing in LuaLS (tip: use hover on RCS, RSC or NSC).

scripts/gen_lsp.lua

@@ -58,14 +58,6 @@ end
 
 ---@param protocol vim._gen_lsp.Protocol
 local function gen_methods(protocol)
-  local output = {
-    '-- Generated by gen_lsp.lua, keep at end of file.',
-    '---',
-    '---@enum vim.lsp.protocol.Methods',
-    '---@see https://microsoft.github.io/language-server-protocol/specification/#metaModel',
-    '--- LSP method names.',
-    'protocol.Methods = {',
-  }
   local indent = (' '):rep(2)
 
   --- @class vim._gen_lsp.Request
@@ -98,6 +90,41 @@ local function gen_methods(protocol)
   table.sort(all, function(a, b)
     return to_luaname(a.method) < to_luaname(b.method)
   end)
+
+  local output = {
+    '-- Generated by gen_lsp.lua, keep at end of file.',
+    '--- @alias vim.lsp.protocol.Method.ClientToServer',
+  }
+  for _, item in ipairs(all) do
+    if item.method and item.messageDirection == 'clientToServer' then
+      output[#output + 1] = ("--- | '%s',"):format(item.method)
+    end
+  end
+
+  vim.list_extend(output, {
+    '',
+    '--- @alias vim.lsp.protocol.Method.ServerToClient',
+  })
+  for _, item in ipairs(all) do
+    if item.method and item.messageDirection == 'serverToClient' then
+      output[#output + 1] = ("--- | '%s',"):format(item.method)
+    end
+  end
+
+  vim.list_extend(output, {
+    '',
+    '--- @alias vim.lsp.protocol.Method',
+    '--- | vim.lsp.protocol.Method.ClientToServer',
+    '--- | vim.lsp.protocol.Method.ServerToClient',
+    '',
+    '-- Generated by gen_lsp.lua, keep at end of file.',
+    '---',
+    '--- @enum vim.lsp.protocol.Methods',
+    '--- @see https://microsoft.github.io/language-server-protocol/specification/#metaModel',
+    '--- LSP method names.',
+    'protocol.Methods = {',
+  })
+
   for _, item in ipairs(all) do
     if item.method then
       if item.documentation then