Is it from the Sunnah for the pilgrim to perform Umrah after completing Hajj from Al-Taneem, following the action of Aisha (may Allah be pleased with her)?

There is no evidence for the legality of repeating Umrah after Hajj from Tan'eem or Ji'ranah; rather, it is better to abstain from doing so. The Prophet, peace and blessings be upon him, and his Companions did not perform Umrah after completing Hajj. A'ishah's, may Allah be pleased with her, Umrah from Tan'eem was to compensate for her missed Umrah due to menstruation. So, whoever is in a situation like A'ishah's, there is no harm in performing Umrah after completing Hajj. However, repeating Umrah after Hajj causes hardship for pilgrims, increases overcrowding and accidents, and goes against the guidance of the Prophet, peace and blessings be upon him.