Is one required to repeat the prayer if one doubted the number of rak'ahs and followed the Imam who added an extra rak'ah out of ignorance of the ruling, and what is the best course of action in such a situation?

The Imam was obliged to perform the prostration of forgetfulness (sujud al-sahw) due to forgetting the first Tashahhud, not to perform an extra rak'ah. The Imam's prayer is valid because he was unaware of the ruling. The prayer of the congregants behind him is also valid, whether they knew of the addition and thought it obligatory to follow, or they doubted it and based their action on the original principle.