What is the ruling on a worshipper (ma'mum) lagging behind the imam in an audible prayer due to completing the remembrance (adhkar) of prostration, which led to the imam beginning to recite Al-Fatiha for the next rak'ah before the worshipper fully stood up, noting that the worshipper recites Al-Fatiha in audible prayers?

The default rule regarding lagging behind the Imam is that it is contrary to the Sunnah. It is only permissible for the worshiper to lag behind if it is to complete an obligatory dhikr. What you did is contrary to the Sunnah. The Sunnah is to promptly follow the Imam and stand up for the raka'ah immediately when he stands for it, without delay, unless you have not recited the obligatory tasbeeh; in that case, you recite it and then follow your Imam. Your prayer is valid as long as you caught up with him in that pillar and he did not precede you in it.