Is it from the Sunnah to raise one's voice in supplication after the prayer has been established, or is it better to say it silently?

The aforementioned supplication is recommended after the adhan (call to prayer). Scholars have differed regarding its recommendation after the iqamah (second call to prayer), but reciting it aloud is not recommended. The manner mentioned in the question is not from the Sunnah. What is required is for a person to recite the supplication silently, not aloud, and not in the manner mentioned.