Is it the Sunnah to proclaim loudly the Takbeer and other supplications after the Tasleem in a congregation Salaah? Give evidence please.

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Whether supplications, uttered after finishing the obligatory prayers, are in a loud voice or not is a matter of difference among the Muslims. Some scholars are of the opinion that these supplications should be recited aloud. Their opinion is based on the Hadith narrated from Ibn Abbas that the companions of the Prophet used to supplicate in a loud voice after finishing the obligatory prayers when the Prophet Muhammad (Peace and blessing be upon him) completed his prayer. Ibn Abbas said: "I used to realize that the prayer had finished when I heard the sound of Takbeer". Imam Nawawi wrote is his explanation of Sahih Muslim that the Hadith of Ibn Abbas is an evidence for those scholars who recommend that the Takbeer and the words of remembrance should be in aloud voice when uttered after the obligatory prayers. Other scholars are of the opinion that supplicating the words of remembrance aloud is not desirable. Imam Shafie said that 'the Prophet raised his voice only for a while to teach the characteristic of the Dikr; he did not continue doing so at all times'.
We perceive that the understanding of Imam Shafie is correct since supplicating aloud is not reported except from Ibn Abbas. This fact proves that the Prophet did not continue these supplications aloud.
Allah knows best.