Make BuilderApplicationTypeInitApplication use handlers rather than services to prevent sending signals.

This was discovered via Sentry issue 3873391462.

If you are on the dashboard, and a builder application is created, it's possible that the BuilderApplicationTypeInitApplication examples page websocket message to be sent to the frontend before the application message is sent.

This can be fixed by swapping the PageService and IntegrationService to their handler counterparts, which don't send signals.