Run and fix codegen tests, make codegen caches per repo root (#64395)

.github/workflows/ci.yml

@@ -298,6 +298,17 @@ jobs:
       - run: git add .
       - run: git diff --staged --exit-code --stat
 
+  codegen:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7.0.1
+      - uses: actions/setup-node@820762786026740c76f36085b0efc47a31fe5020 # v7.0.0
+        with:
+          node-version: '>=22.18.0'
+      - uses: ./.github/actions/setup-go
+      - run: npm ci
+      - run: npx hereby test:codegen
+
   tidy:
     runs-on: ubuntu-slim
     steps:
@@ -341,6 +352,7 @@ jobs:
     if: ${{ always() }}
     needs:
       - build
+      - codegen
       - release-build
       - extension
       - format