What is the ruling on repeating the takbirat al-intiqal (transition takbir) and does one perform sujud al-sahw (prostration of forgetfulness) for it?

The place for the takbirat al-intiqal (transition takbirs) is during the movement to the rukn (pillar/integral part of prayer). So, whoever pronounces them in their proper place is not required to perform the prostration of forgetfulness (sujud al-sahw), and if they repeat them, sujud al-sahw is still not obligatory upon them.

As for whoever forgets a takbirat al-intiqal until they reach the rukn, its proper place has passed, and sujud al-sahw is obligatory upon them.

And whoever intentionally omits it until they reach the rukn, their prayer becomes invalid according to the Hanbalis, while it remains valid according to the majority of scholars who consider it a sunnah (recommended act).

And it is advised for the one afflicted by waswas (obsessive whispering) to act upon the opinion of the majority.