Ramban Shaar Gemul inyan din rosh hashana
on Rosh Hashana a person's deeds are weighed and he is written and
sealed for zechut (merit) or chova (the opposite) in this world
according to what he deserves in this world. and when he dies, his
deeds are weighed and he is judged on the portion he deserves in the
world of souls.
this is a partial answer as to why we still pray to do teshuva, be forgiven, improve our ways, etc. of the things relevant to the next world.
Another answer which addresses the question as to why we ever pray at all. from the Manoach Halevavos commentary (Chovos Halevavos 3:3)
Manoach Halevavos: If we were not commanded in prayer by the torah and
the Rabbinical decrees, we would not know through our understanding
what would be the order of the tefila, shacharit (morning), mincha
(afternoon), and arvit (evening), and the other times. And even prayer
itself, the understanding does not dictate that we should pray to G-d,
because the understanding obligates that G-d gives to each creature
and each thing in the world the portion fitting for it. And if it is
not fitting for it, prayer should not help in this. Furthermore,
according to the divine wisdom (Kabala), and the Moray Nevuchim wrote
on this (Part 1 ch.5), that G-d does not "change". Hence, the whole
matter of prayer seems to the understanding as if there is "change" in
G-d, similar to a request which a man begs before a flesh and blood
king, to arouse favor and pity in the heart of the king. All this does
not apply by G-d. Therefore, he wrote that if the torah did not
command this, and that we did not see from the torah that prayer does
help, regarding the prayer of Avraham, Yitzchak, Yaakov, Moshe, and
others, and that our Sages did not institute its order, we would not
know at all through the understanding neither its order not its
matter. The reason we have been commanded in it is hidden, it is
among the hidden precepts of the torah. It has great benefits to
arouse a person to awareness of G-d's existence, and His almighty
power, and that it is proper to serve Him, and many other fundamentals
and good traits which are aroused through prayer. In kabala it is
known that by a hitorerut (stimulus) from below, one causes a
hitorerut (stimulus) above