What is the ruling on the prayer of someone who inadvertently missed the first tasleem with the Imam, and prostrated directly for the prostration of forgetfulness, and then said the tasleem with the Imam thereafter?

It would have been better for you to say the Taslim (definition) (salutation of peace) as soon as you remembered, and then join the Imam in the prostration of forgetfulness (Sujud (definition) al-Sahw). Nevertheless, what you did does not invalidate your prayer. Your prayer is valid because the Imam bears the forgetfulness of the ma'mum (follower) that does not invalidate the prayer, and the ma'mum is not required to perform Sujud al-Sahw. The majority of scholars hold the view that if a ma'mum forgets something while following the Imam, there is no Sujud for him.