ci: split checks across pr/merge group/main (#3405)

.github/workflows/integration.yml

@@ -1,7 +1,4 @@
 on:
-  push:
-    branches:
-      - main
   pull_request:
   merge_group:
 
@@ -66,6 +63,8 @@ jobs:
 
   sync:
     name: sync / 100k blocks
+    # Only run sync tests in merge groups
+    if: github.event_name == 'merge_group'
     runs-on: ubuntu-latest
     env:
       RUST_LOG: info,sync=error
@@ -95,7 +94,7 @@ jobs:
     if: always()
     name: integration success
     runs-on: ubuntu-latest
-    needs: [test, sync]
+    needs: [test]
     steps:
       - name: Decide whether the needed jobs succeeded or failed
         uses: re-actors/alls-green@release/v1