بِسۡمِ ٱللَّهِ ٱلرَّحۡمَٰنِ ٱلرَّحِيمِ
The evidence that small movements, or repeated movements that are not continuous, do not invalidate the prayer
Narrated AbuSa'id al-Khudri:
While the Messenger of Allah (ﷺ) was leading his Companions in prayer, he took off his sandals and laid them on his left side; so when the people saw this, they removed their sandals. When the Messenger of Allah (ﷺ) finished his prayer, he asked: What made you remove your sandals? The replied: We saw you remove your sandals, so we removed our sandals.The Messenger of Allah (ﷺ) then said: Gabriel came to me and informed me that there was filth in them. When any of you comes to the mosque, he should see; if he finds filth on his sandals, he should wipe it off and pray in them. (https://sunnah.com/abudawud:650)
Narrated Anas:
The Prophet (ﷺ) said, "Whenever anyone of you offers his prayer he is speaking in private to his Lord. So he should not spit to his right but under his left foot." Qatada said, "He should not spit in front of him but to his left or under his feet." And Shu`ba said, "He should not spit in front of him, nor to his right but to his left or under his foot." Anas said: The Prophet (ﷺ) said, "He should neither spit in the direction of his Qibla nor to his right but to his left or under his foot." https://sunnah.com/bukhari:531
Narrated Aisha, Ummul Mu'minin:
The Messenger of Allah (ﷺ) was praying with his door bolted. I came and asked to have the door opened. He walked and opened the door for me. He then returned to his place for prayer. He (the narrator Urwah) mentioned that the door faced the qiblah. https://sunnah.com/abudawud:922
Abu Qatada reported: I saw the Messenger of Allah (ﷺ) saying the prayer while he was carrying Umama, daughter of Zainab, daughter of the Messenger of Allah (ﷺ). and Abu'l-'As b. al-Rabi'. When he stood up, he took her up and when he prostrated he put her down, Yahya said: Malik replied in the affirmative. https://sunnah.com/muslim:543a
Reference: https://islamqa.info/en/answers/12683/moving-while-praying