What is the ruling on excessive supplication after prayers to the extent of considering it an obligation, and does this cause lethargy in prayer?

Supplicating to Allah and showing humility to Him is among the best acts of worship. Through it, Allah fulfills needs and repels evil. Allah has promised the supplicant either a response, or to save their supplication for the Hereafter, or to avert evil from them. It is commendable to be diligent in supplication at times when prayers are likely to be answered, such as after the Adhan, during prostration (sujud), and at the end of prayers. Having good thoughts about Allah leads to good. However, supplication at these times is not an obligation. It is recommended to be persistent in it, even if little, especially with the supplications reported from the Prophet (peace be upon him).