Is it obligatory to repeat the prayer after standing up and returning to a seated position, then performing the Taslim and the prostration of forgetfulness (Sujud al-Sahw) without reciting the Tashahhud after returning?

What you did is correct, and you are not required to repeat the prayer. As long as you recited the tashahhud before standing up, you are obligated to return to a seated position and send blessings upon the Prophet, peace be upon him, if you had not already done so. If you had already sent blessings upon him, then do not repeat the tashahhud and the blessings upon him. Rather, you prostrate for forgetfulness (sujud al-sahw) before or after the taslim. In this case, it is preferable for it to be after the taslim because it is due to an addition. So, you make the taslim, then prostrate for forgetfulness, then make the taslim.