Is the audible glorification of Allah after the Imam recites the first verse of Surat Al-A'la in the Friday prayer a Sunnah, or is there no evidence to support it?

It is prescribed for one who recites the verse: ﴿Glorify the Name of your Lord, the Most High﴾ (Surat Al-A'la, 87:1) to say: "Subhana Rabbiyal-A'la (Glory be to my Lord, the Most High)." This has been reported in narrations from the Prophet, peace and blessings be upon him, and from the Companions and the Tabi'in.

The Shafi'is and Hanbalis hold the view that it is recommended for the reciter to glorify Allah when reaching a verse of glorification, to ask when reaching a verse of asking, and to seek refuge when reaching a verse of seeking refuge. This applies whether in or outside of prayer, in obligatory or supererogatory prayers, and for the Imam, the congregant, and the individual praying alone.

However, the Hanbalis consider it recommended in supererogatory prayers, and permissible in obligatory prayers without being recommended, because there is no report that the Prophet, peace and blessings be upon him, did so in obligatory prayers. Sheikh Ibn Uthaymin held the view that it is sunnah (recommended practice) in supererogatory prayers, and permissible in obligatory prayers but not sunnah, because the Prophet, peace and blessings be upon him, did not do it in obligatory prayers, and no such report has been transmitted from him.

Based on this, the congregants saying "Subhana Rabbiyal-A'la" when the Imam recites (Glorify the Name of your Lord, the Most High) is considered sunnah by the Shafi'is and permissible by the Hanbalis. However, it is not prescribed to raise one's voice with it; rather, it should be done silently, due to the potential for causing disturbance.