test Depot runners for team commits (#6394)

Co-authored-by: ConnorYoh <[email protected]>

.github/workflows/e2e-live.yml

@@ -5,13 +5,23 @@ name: Playwright E2E (live backend)
 # server.
 on:
   workflow_call:
+    inputs:
+      depot_cores:
+        description: "Depot runner vCPU count (used in runs-on). Override for benchmarking."
+        required: false
+        type: string
+        default: "8"
 
 permissions:
   contents: read
 
 jobs:
+  pick:
+    uses: ./.github/workflows/_runner-pick.yml
+
   playwright-e2e-live:
-    runs-on: ubuntu-latest
+    needs: pick
+    runs-on: ${{ needs.pick.outputs.is_fork == 'true' && 'ubuntu-latest' || format('depot-ubuntu-24.04-{0}', inputs.depot_cores || '8') }}
     timeout-minutes: 30
     steps:
       - name: Harden Runner