What is the ruling on the prayer of one who missed the first rak'ah and did not perform the pre-emptive prostration with the Imam, who did not sit for the middle tashahhud but remained sitting until the Imam said the taslim, then completed his prayer and performed the pre-emptive prostration?

You should have prostrated with the Imam when he performed the prostration of forgetfulness (sujud as-sahw), and then performed another prostration at the end of your prayer, because that is the place for the prostration of forgetfulness. The validity of your prayer is a matter of scholarly disagreement, due to their differing views on the obligation of this prostration. Therefore, it is preferable to repeat the prayer as a precautionary measure.