Is it permissible to change the intention of a four-rak'ah obligatory prayer to a supererogatory one, then sit for the tashahhud and say the taslim in the third rak'ah due to disturbance, and then perform the two prostrations of forgetfulness (sujud al-sahw) thereafter?

You should seek a place for your prayers where there are no distractions. It is important to note that scholars have differed regarding the ruling on changing an obligatory prayer into a supererogatory one. Some have prohibited it, while others have deemed it reprehensible except for a valid reason, such as joining a congregation. This is the view of the Hanbalis. What you mentioned about disturbance is not an excuse that permits interrupting an obligatory prayer or changing it into a supererogatory one, unless the disturbance is so severe that it prevents devotion (khushu'). In that case, it is permissible to interrupt it and change it into a supererogatory prayer in order to perform the obligatory prayer in a more complete manner, and this is a valid reason. Sheikh Al-Uthaymeen said: "Interrupting an obligatory prayer to move to something better is not forbidden; rather, it may be commanded." If you change the obligatory prayer into a supererogatory one, then the prostration of forgetfulness (sujood as-sahw) is not prescribed for you. It is also important to note the difference of opinion regarding performing voluntary prayers with one, three, or five rak'ahs. You should avoid this disagreement by completing the prayer in even units (shaf'an) when a valid reason is found that permits interrupting the obligatory prayer and changing it into a supererogatory one.