ci: add experimental Nx affected workflow (#16389)

* ci: add experimental Nx affected workflow

Adds .github/workflows/nx.yml to run \`nx affected\` on pull requests,
testing only changed libraries for build, lint, and test targets.

This prevents regressions of the library configuration issues discovered
in the systematic Nx library audit and ensures proper library builds in CI.

Features:
- Uses nrwl/nx-set-shas for accurate affected project detection
- Tests build, lint, and test targets
- Runs on PR open/synchronize events
- Helps catch package.json path bugs before merge

* review: get node version from .nvmrc

Author: addisonbeck

.github/workflows/nx.yml

@@ -0,0 +1,41 @@
+name: Experimental Nx CI
+on:
+  pull_request:
+    types: [opened, synchronize]
+
+permissions:
+  contents: read
+
+jobs:
+  nx-experiment:
+    name: Run Nx Affected Tasks
+    runs-on: ubuntu-22.04
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
+        with:
+          fetch-depth: 0
+      
+      - name: Get Node Version
+        id: retrieve-node-version
+        working-directory: ./
+        run: |
+          NODE_NVMRC=$(cat .nvmrc)
+          NODE_VERSION=${NODE_NVMRC/v/''}
+          echo "node_version=$NODE_VERSION" >> $GITHUB_OUTPUT
+
+      - name: Set up Node
+        uses: actions/setup-node@39370e3970a6d050c480ffad4ff0ed4d3fdee5af # v4.1.0
+        with:
+          cache: 'npm'
+          cache-dependency-path: '**/package-lock.json'
+          node-version: ${{ env._NODE_VERSION }}
+      
+      - name: Install dependencies
+        run: npm ci
+      
+      - name: Set Nx SHAs for affected detection
+        uses: nrwl/nx-set-shas@826660b82addbef3abff5fa871492ebad618c9e1 # v4.3.3
+      
+      - name: Run Nx affected tasks
+        run: npx nx affected -t build lint test