Prayer: Do mustaḥabb prayers have to be recited loudly or quietly based on their corresponding obligatory prayers?

Practical Laws of Islam as per the teachings of Imam Khamenei

Prayer: Do mustaḥabb prayers have to be recited loudly or quietly based on their corresponding obligatory prayers?

English:

Question #472:

Is there any proof for the opinion that mustaḥabb prayers of loud prayers should be recited loudly? What about quiet recitation of mustaḥabb prayers pertaining to the quietly recited prayers? If yes, suppose that a mustaḥabb prayer which belongs to a loud prayer, for instance, is recited quietly. Will it be correct? What about the reverse case? We would appreciate your kind reply.

Answer #472:

It is mustaḥabb to recite the mustaḥabb prayers of loud obligatory prayers loudly and those of quiet ones quietly. If they are recited otherwise they are also correct.

-Imam Khamenei, Practical Laws of Islam, Importance and Conditions of Prayer