What should one do if they made a mistake in the transitional takbeer (takbeerat al-intiqal) during prayer, such as saying: (Allahu Akbar) forgetfully, and remembered their mistake moments before prostrating?

What happened regarding the mistake in the transitional takbir (Allahu Akbar) does not necessitate anything according to the majority of scholars. Your prayer is valid, and you are not required to perform the prostration of forgetfulness (sujud al-sahw). However, according to the Hanbalis, it is prescribed for you to perform the prostration of forgetfulness before the taslim (salutation of peace) for omitting an obligatory act, but omitting the prostration of forgetfulness here does not invalidate the prayer. If you are a ma'mum (follower in congregational prayer), you are not required to perform the prostration of forgetfulness because the Imam bears it on your behalf.