Is the Fajr prayer valid if the Imam bowed at the spot of the prostration of recitation, then performed it after being alerted by the congregants, and did not perform the prostration of forgetfulness (sujud al-sahw)?

The Imam was obligated to continue his bowing (rukūʿ) and not abandon it for the prostration of recitation (sujūd al-tilāwah), because moving from a pillar (rukn) to something lesser than it invalidates the prayer if the person is intentionally aware of the ruling. However, if they are ignorant or forgetful, the prayer is valid. Since the Imam's action is presumed to be unintentional, your prayer is valid. Nevertheless, the prostration of forgetfulness (sujūd al-sahw) should have been performed after the salutation (salām) due to the addition of the bowing. Sujūd al-sahw is waived if there is a lengthy interval, or by exiting the mosque, or it can be performed even after a long interval according to some scholars. The prayer is valid whether the Imam intentionally omitted the prostration or not, because sujūd al-sahw is a sunnah according to the majority of scholars.