What is the ruling on re-reading something other than the Qur’an in prayer when correcting a mistake or doubting it, such as repeating the opening takbir or the taslim?

The transitional takbeer and tahmeed are obligatory according to some scholars, such as the Hanbalis. So, whoever makes an error in them that changes the meaning, must rectify them before their time expires. The majority of scholars, however, hold that they are Sunnah, so whoever intentionally omits them, their prayer is valid.

The tasleem (salutation) at the end of the prayer is a pillar. Whoever makes an error in it that changes the meaning must repeat it, otherwise their prayer is invalid.

Sending blessings upon the Prophet, peace be upon him, in the final tashahhud is a pillar according to a group of scholars. So, whoever makes an error in it that changes the meaning must repeat it, otherwise their prayer is invalid.

Doubt about an error should not be paid attention to, and if obsessive thoughts (waswas) become frequent, they should be ignored.