Do the swinging hands after rising from rukūʿ until prostrating invalidate ṭumaʾnīnah (tranquility), and does a person who forgot and prayed for years in this manner fall under the fatwa of Shaykh al-Islam Ibn Taymiyyah regarding non-repetition (of prayers)?

"Tranquility is a pillar in the actions of prayer, like the occurrence of stillness, even if slight, or equivalent to the duration of the obligatory remembrance (dhikr). It does not necessarily mean that no part of the body moves. If the back becomes steady during standing for the duration of performing the obligatory dhikr, then tranquility has been achieved. A slight movement of the hands does not harm, and past prayers do not need to be repeated."