What is the ruling on performing one of the Sunan (plural of Sunnah) of prayer out of its proper place, such as raising the hands during the Tashahhud, whether forgetfully or intentionally, and does that necessitate a prostration of forgetfulness (sujud al-sahw)?

Raising the hands during prostration is not legislated and does not invalidate the prayer. It also does not necessitate a prostration of forgetfulness, whether the worshipper does it intentionally or out of forgetfulness. This is because it is not among the actions that invalidate the prayer when done intentionally, nor does it obligate prostration due to forgetfulness.