Question: [Sunday 17th Elul, 5780]
I forgot to recite Kadesh and Vehaya Ki Yiviacha while wearing Rabbeinu Tam. What should I do?
There is no need to re-wear Rabbeinu Tam and recite it.
The reason: This matter is just a custom and not required from the letter of the law. Thus, certainly, we do not require one to re-wear the Tefillin due to it.
Sources: See M”A 25:6 based on Sifri; Siddur Admur regarding Tefillin of Rabbeinu Tam; M”B 25:16; See here: https://shulchanaruchharav.com/halacha/chapter-1-the-general-laws-of-tefillin/ by footnote 102-112