Is it permissible for someone who forgets the number of rak'ahs or the first tashahhud in prayer to change their intention from obligatory to supererogatory and then repeat the obligatory prayer, or to abandon the prayer and start it anew?

It is not permissible to exit a fard (obligatory) prayer without a legitimate Shar'i (Islamic legal) excuse. A fard prayer should not be converted into a voluntary (nafl) prayer absolutely unless there is a valid purpose, such as catching the congregational prayer. If there is no valid purpose, it is permissible but disliked (makruh).

Changing the intention from fard to nafl due to lack of khushu' (devotional humility) opens the door to waswasa (whispers/obsessive thoughts). The Prophet (peace be upon him) did not command someone who experienced frequent waswasa to stop their prayer or convert it to nafl; rather, he commanded them to build upon certainty and perform the prostration of forgetfulness (sujud as-sahw).

The remedy for waswasa is through striving (mujahadah), seeking refuge in Allah, and spitting lightly to the left three times. If doubt becomes frequent, it should be ignored, and the prayer should be built upon the prevailing assumption.