chore(build-system-test): Run build system tests pre-release and on schedule (#5706)

Author: esauerbo

.github/workflows/build-system-test-react-native.yml

@@ -6,8 +6,6 @@ permissions:
   id-token: write # This is required for aws-actions/configure-aws-credentials
 
 on:
-  push:
-    branches: ['main']
   schedule:
     - cron: '0 */2 * * *' # Run on the first minute of each even numbered hour