doc: use npm-published version of doc-kit

.github/workflows/tools.yml

@@ -121,14 +121,6 @@ jobs:
             run: |
               make corepack-update
               echo "NEW_VERSION=$(node deps/corepack/dist/corepack.js --version)" >> $GITHUB_ENV
-          - id: doc-kit
-            subsystem: tools
-            label: tools
-            run: |
-              ./tools/dep_updaters/update-doc.sh > temp-output
-              cat temp-output
-              tail -n1 temp-output | grep "NEW_VERSION=" >> "$GITHUB_ENV" || true
-              rm temp-output
           - id: googletest
             subsystem: deps
             label: dependencies, test

Makefile

@@ -384,7 +384,7 @@ ifeq ($(OSTYPE),os400)
 DOCBUILDSTAMP_PREREQS := $(DOCBUILDSTAMP_PREREQS) out/$(BUILDTYPE)/node.exp
 endif
 
-DOC_KIT ?= tools/doc/node_modules/@nodejs/doc-kit/bin/cli.mjs
+DOC_KIT ?= tools/doc/node_modules/@node-core/doc-kit/bin/cli.mjs
 
 node_use_openssl_and_icu = $(call available-node,"-p" \
 			 "process.versions.openssl != undefined && process.versions.icu != undefined")