Are the text messages sent by the Execution App real?

Not necessarily.

Under normal circumstances, the court will not send text messages. They will all be written documents or call you to inform you of certain things. They will not send text messages. They will issue some written documents either by mail or by sending someone to deliver them directly. In the workplace, everyone now knows that text messages cannot be trusted, and the court will not send text messages. But there are exceptions to everything. If you have not touched the law, it is better to call the police.