Is there any Sharia-based or Sunnah-based evidence for the desirability of praying two rak'ahs as seeking forgiveness after completing the recitation of the Quran to cover any oversight or error in the recitation?

There is no two-rak'ah prayer after reciting the Qur'an in the Sunnah, and no scholar has ever mentioned such a thing. Therefore, it is not prescribed for the reciter of the Qur'an to pray two rak'ahs after or before the recitation due to lack of evidence. The fundamental principle regarding acts of worship is that they are tawqifī (requiring explicit divine instruction) until a legal proof is established, in accordance with the Prophet's (peace be upon him) saying: "Whoever introduces into this matter of ours that which is not from it, it is rejected."