Does compiling the variant readings mean synthesizing the authentic narrations heard from the Tabi'in (successors) from the Companions, such that a specific reading results from it? And did the Imams choose different variant readings from a single verse that were authentically transmitted from the Prophet (peace be upon him)? And what is the correct meaning of choosing variant readings?

Imam Nafi' used to teach his students what two or more of his shaykhs had agreed upon, and he would leave what only one had narrated. This is not an innovation; rather, it is a selection of the most authentic narrations. Recitation (qira'ah) is a followed Sunnah, and the recitations (qira'at) are divinely ordained (tawqifiyyah), not optional. The reciters (qurra') used to teach students with different variations. For example, Nafi' taught Qalun variations that he did not teach Warsh, and vice versa. Similarly, Asim taught Shu'bah variations that he did not teach Hafs, and vice versa. Hafs once asked Asim about the difference in his recitation compared to Abu Bakr, and Asim replied that he taught Hafs the recitation of Abu Abd al-Rahman al-Sulami from Ali ibn Abi Talib, and he taught Abu Bakr the recitation of Zirr ibn Hubaysh from Ibn Mas'ud. This difference in teaching recitations is well-established from the Imams and even from the Prophet, peace and blessings be upon him, as in the story of Umar and Hisham ibn Hakim when their recitations differed, and the Prophet, peace and blessings be upon him, approved both, saying: "Indeed, this Qur'an has been revealed in seven ahruf (modes of recitation), so recite whatever is easy from it."