What is the expiation for not fulfilling a vow to perform 200 rak'ahs of prayer and complete the recitation of the Qur'an twice after confirming recovery from illness, knowing that advanced medical examinations were not conducted, and recovery was confirmed?

Praise be to Allah, who has granted you well-being. Delaying a time-bound vow beyond its stipulated time, without necessity or a valid excuse, is impermissible. Whoever does so incurs sin and is obligated to repent, offer an expiation for a broken oath (kaffarat yameen), and then fulfill the vow.

Therefore, you must repent to Allah Almighty if you delayed fulfilling the vow beyond its specified time without a legitimate Shar'i excuse. You are also required to offer an expiation for a broken oath (feeding ten poor persons, or clothing them, or emancipating a slave; or fasting for three days if you cannot find any of these), and fulfill the vow as soon as possible.