Praise be to Allah.
What is meant by the being at ease that is an essential part of the prayer, without which the prayer is not valid, is stillness of the limbs and pausing, even for a moment. According to some scholars, that should last for as long as it takes to recite the obligatory dhikr.
So when the worshipper leans forward to bow, and pauses for a brief moment, and his limbs become still, then he has attained being at ease.
If he remains still for a while, until he says “Subhaan Rabbiy al-‘Azeem (Glory be to my Lord the Almighty)” once, then he has attained being at ease according to the second scholarly view, which says that it should last for as long as it takes to recite the obligatory dhikr.
But if his bowing is like a pendulum, meaning that he bows and then rises without even pausing for a moment, then he has not attained being at ease, and his prayer is not valid.
Being at ease is not an action of the heart, so it is not the same thing as khushoo‘ (proper focus and humility in prayer), or feeling of calm with or without releasing the breath (breathing out); rather it is what has been explained above, namely pausing with stillness of the limbs.
If one who is praying behind an imam moves so slowly that he lags behind his imam, his action is not acceptable, even if he does that in order to focus his mind and attain comfort in his heart.
If the imam is clearly moving so fast that he is not fulfilling the condition of being at ease in his prayer, and he does not pause so that his limbs become still in each essential part of the prayer, then the prayer offered behind him is not valid, because he is not fulfilling one of the essential conditions of the prayer (namely being at ease in the prayer).
But if his speed is relative, in the sense that he is being at ease for the length of time that is required, then it is permissible to pray behind him, and the one who is praying behind him must follow him in his movements without lagging behind.
If you lag behind him only a little, in order to attain being at ease as is required, then there is no blame on you for that.
Moreover, you have to strive to attain both things: following the imam, and being at ease in your movements.
Please see also the answer to question no. 219808 – in particular, the third issue discussed there.
And Allah knows best.