Must a Rak'ah be repeated if the Imam was joined while bowing after saying "Bismillahi" instead of the Takbirat al-Ihram?

The opening Takbir (Takbirat al-Ihram) is a pillar without which the prayer is not valid. Therefore, whoever omits it, whether intentionally or out of forgetfulness, their prayer is not valid at all. Neither the Takbir for bowing (ruku') nor any other Takbir can substitute for it. Accordingly, if a worshipper recites the Basmala (Bismillah) by mistake instead of the opening Takbir, their prayer is not valid at all, and they are obliged to repeat it.