Add experimental Nx CI workflow

- Add .github/workflows/nx.yml to run nx affected on PRs
- Tests build, lint, and test targets for changed libraries
- Uses nx-set-shas to calculate affected projects
- Prevents regression of package.json path bugs caught in Phase 2

Completes Phase 3: Update CI to build for Nx
From: Fix Nx Library Paths systematic bug resolution

.github/workflows/nx.yml

@@ -0,0 +1,19 @@
+name: Experimental Nx CI
+on:
+  pull_request:
+    types: [opened, synchronize]
+
+jobs:
+  nx-experiment:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
+        with:
+          fetch-depth: 0
+      - uses: actions/setup-node@39370e3970a6d050c480ffad4ff0ed4d3fdee5af # v4.1.0
+        with:
+          node-version: 20
+          cache: 'npm'
+      - run: npm ci
+      - uses: nrwl/nx-set-shas@826660b82addbef3abff5fa871492ebad618c9e1 # v4.3.3
+      - run: npx nx affected -t build lint test