ci: run the browser suite as two shards

The single job passed at about eighteen minutes against a twenty-minute
cap, and the settings geometry measurements pushed it over, so the run
died at the timeout with everything to that point green. Same remedy as
the integration suite, split rather than raise: two Playwright shards,
each with its own database and production build, and a gate job carrying
the exact name branch protection requires that fails when any shard
failed or was cancelled.

.github/workflows/e2e.yml

@@ -15,9 +15,19 @@ concurrency:
   cancel-in-progress: true
 
 jobs:
-  e2e:
+  # The suite outgrew the runner the same way the integration suite did: the
+  # single job passed at ~18 minutes against a 20-minute cap, and the settings
+  # geometry measurements pushed it over. Same remedy, split rather than raise:
+  # two Playwright shards, each with its own database and production build, and
+  # a gate job below that carries the exact name branch protection requires.
+  shard:
     runs-on: ubuntu-latest
     timeout-minutes: 20
+    strategy:
+      fail-fast: false
+      matrix:
+        shard: [1, 2]
+    name: e2e shard ${{ matrix.shard }}/2
     services:
       postgres:
         image: postgres:16-alpine
@@ -87,7 +97,7 @@ jobs:
       # chart-runtime boundary (a duplicated ~92 KB gz recharts chunk).
       - run: pnpm bundle-check
 
-      - run: pnpm exec playwright test
+      - run: pnpm exec playwright test --shard=${{ matrix.shard }}/2
         env:
           E2E_BASE_URL: http://localhost:3000
 
@@ -99,3 +109,19 @@ jobs:
           path: playwright-report/
           retention-days: 7
           if-no-files-found: ignore
+
+  # Branch protection requires a check named exactly "e2e". This job carries
+  # that name and answers for both shards: it fails when any shard failed or
+  # was cancelled, so a half-green matrix cannot satisfy the gate.
+  e2e:
+    runs-on: ubuntu-latest
+    needs: shard
+    if: always()
+    timeout-minutes: 5
+    steps:
+      - name: Every shard finished green
+        run: |
+          if [ "${{ needs.shard.result }}" != "success" ]; then
+            echo "shard result: ${{ needs.shard.result }}"
+            exit 1
+          fi