Is the punishment of stoning not mentioned in the Qur’an, and would it not have been more appropriate for it to be mentioned therein, given that it is more severe than flogging?

It is authentically established in the sound Sunnah that Allah revealed the verse of stoning for the married fornicator, and it was a Qur'anic recitation. Then Allah abrogated its wording while retaining its ruling, as was narrated from Umar ibn al-Khattab, may Allah be pleased with him. Scholars have mentioned reasons for the abrogation of its wording and the retention of its ruling, among them being a test for the Ummah and an examination of the strength of its faith and its prompt obedience to its Lord. Another reason is to lighten the burden on the Ummah by not making its recitation widely known, while its ruling remains, because it is one of the most severe rulings.