It is not permissible to describe it as a Bid’ah (innovation) because it is never claimed to be a Sunnah phrase and it is included under the principle of general supplication for special events. We great people with the phrase ” Eid Mubarak” on Eid day even though it was not reported in the Sunnah that our beloved Prophet Muhammad, may peace and blessings be upon him, used to say it and the scholars did not say it was a Bid’ah to say so. The same ruling applies to Jummah day since it is a weekly Muslim holiday.
It was narrated that Ibn ‘Abbas said:
“The Messenger of Allah (ﷺ) said: ‘This day is an ‘Eid (festival) which Allah has ordained for the Muslims. Whoever comes to Friday (prayer), let him take a bath and if he has perfume then let him put some on. And upon you (I urge you to use) is the tooth stick.” Sunan Ibn Majah 1098
Therefore, we do not see any objection to this supplication. Rather, it is a kind supplication that increases the bonds of brotherhood and love among Muslims. However, one should beware of attributing this supplication to the Prophet, may God’s prayers and peace be upon him; because there was no text from him indicating such phrase and claiming it to be a Sunnah phrase to announce on the day of Friday.