Uthman (﵁) was the first to implement the second Adhan on the day of Jumu'ah.
Narrated Sa'ib ibn Yazid (﵁): He said that during the time of the Prophet ﷺ, Abu Bakr (﵁), and Umar (﵁), the Adhan for Jumu'ah day was given immediately after the Imam sat on the Minbar. However, during the caliphate of Uthman (﵁), when the population increased, they added a third Adhan (including the Iqamah) from 'Az-Zawra'. Thereafter, the matter became established as such." (Bukhari, Vol:3, Page: 422).
إنَّ الأذَانَ يَومَ الجُمُعَةِ كانَ أوَّلُهُ حِينَ يَجْلِسُ الإمَامُ، يَومَ الجُمُعَةِ علَى المِنْبَرِ في عَهْدِ رَسولِ اللَّهِ صَلَّى اللهُ عليه وسلَّمَ، وأَبِي بَكْرٍ، وعُمَرَ رَضِيَ اللَّهُ عنْهمَا، فَلَمَّا كانَ في خِلَافَةِ عُثْمَانَ بنِ عَفَّانَ رَضِيَ اللَّهُ عنْه، وكَثُرُوا، أمَرَ عُثْمَانُ يَومَ الجُمُعَةِ بالأذَانِ الثَّالِثِ، فَأُذِّنَ به علَى الزَّوْرَاءِ، فَثَبَتَ الأمْرُ علَى ذلكَ.
In the commentary of this Hadith, Ibn Hajar (﵀) writes: It is clear that on that very day, action was taken according to Uthman's (﵁) instruction in all regions (Fathul Bari, Vol: 3, Page: 424).
Imam Badruddin al-Ayni (﵁) says: "Since the Sahabah agreed with Uthman (﵁) on the matter of the Adhan and did not criticize it, it became a Sukuti Ijma' (silent consensus)" (Umdatul Qari).
وموافقة سائر الصحابة له بالسكوت وعدم الإنكار؛ فصار إجماعا سكوتيا(عمدة القاري)
Ibn Rajab al-Hanbali (﵀) writes: The phrase 'the matter became established as such' indicates that since Uthman (﵁) implemented the said Adhan, it became established and was not abandoned thereafter. This informs us that Ali (﵁) also approved it. Therefore, two Caliphs among the Khulafa'ur Rashidun (Rightly Guided Caliphs) were in agreement in performing it (Fathul Bari, Ibn Rajab. 6/211).
Sheikh Zainuddin Makhdoom explains in Fathul Mu'in: 'Uthman (﵁) implemented the Adhan before the Khatib (speaker) ascended the Minbar when the population increased. Therefore, it is said to be Sunnah when there is a need, such as attendance for Jumu'ah depending on this Adhan' (Fathul Mu'in, Page: 98).
In short, the approach of the Wahhabis, who reject the Adhan – which Uthman (﵁) put into practice and which global Muslims accepted and have been observing – as an innovation (Bid'ah) solely because the Prophet ﷺ did not do it, is completely wrong.