Must I perform the prostration of forgetfulness (sujood as-sahw) if I pray behind imams who do not pronounce the transitional takbeers or the tasmee’ (saying ‘Sami’ Allahu liman hamidah’) in their proper places, given my conviction that they are obligatory?

The prayer of the imams is valid even if they omit the transition takbirat (saying "Allahu Akbar" when moving between prayer postures) or perform them incorrectly. It is not prescribed to abandon praying behind someone who omits some matters over which there is disagreement, nor is sujud al-sahw (prostration of forgetfulness) prescribed after their prayer. The imams have explicitly stated the permissibility of praying behind someone who differs in furu' (branches of Islamic law). Sheikh al-Islam Ibn Taymiyyah said: "It is permissible for followers of different madhhabs (schools of thought) to pray behind one another. None of the Salaf (early Muslims) said that they should not pray behind one another, and whoever denies this is an innovator and misguided." A Muslim should only clarify the Sunnah.