fix: Refine and simplify markdown pipeline (#47416)

.github/workflows/docs-markdown-manifest-sync.yml

@@ -1,55 +0,0 @@
-name: Docs Markdown Manifest Sync
-
-on:
-  pull_request:
-    branches: ['master']
-    paths:
-      - 'apps/docs/content/guides/**/*.mdx'
-      - 'apps/docs/content/troubleshooting/**/*.mdx'
-      - 'apps/docs/internals/generate-markdown-manifest.ts'
-      - 'apps/docs/internals/markdown-sources.ts'
-      - 'apps/docs/lib/markdown-manifest.ts'
-
-# Cancel old builds on new commit for same workflow + branch/PR
-concurrency:
-  group: ${{ github.workflow }}-${{ github.event.pull_request.number || github.ref }}
-  cancel-in-progress: true
-
-permissions:
-  contents: read
-
-env:
-  CI: true
-
-jobs:
-  check:
-    name: Check apps/docs/lib/markdown-manifest.ts is in sync
-    runs-on: blacksmith-4vcpu-ubuntu-2404
-
-    steps:
-      - uses: actions/checkout@08eba0b27e820071cde6df949e0beb9ba4906955 # v4.3.0
-        with:
-          persist-credentials: false
-          sparse-checkout: |
-            apps/docs
-            examples
-            packages
-            supabase
-            patches
-
-      - uses: pnpm/action-setup@41ff72655975bd51cab0327fa583b6e92b6d3061 # v4.2.0
-        name: Install pnpm
-        with:
-          run_install: false
-
-      - name: Use Node.js
-        uses: actions/setup-node@49933ea5288caeca8642d1e84afbd3f7d6820020 # v4.4.0
-        with:
-          node-version-file: '.nvmrc'
-          cache: 'pnpm'
-
-      - name: Install deps
-        run: pnpm install --frozen-lockfile
-
-      - name: Verify markdown manifest is up to date
-        run: pnpm --filter docs check:markdown-manifest