What is the ruling on the prayer of someone who made a mistake and forgot a part of the Iqamah through the loudspeakers in the mosque?

Your mistake and forgetting some of the Iqamah (definition) does not invalidate the prayer. The Iqamah is a confirmed Sunnah (definition), and prayer is not invalidated by intentionally omitting it entirely, let alone by accidentally omitting part of it. The correct view is that of the majority, which states that the prayer is valid in this case. What you did out of error or forgetfulness carries no sin, for the Prophet, peace and blessings be upon him, said: "Indeed, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are coerced into."