An important variable you should look at when looking to replace a fork on your existing bike
is the axel to crown height. If the axel to crown height is changed,
so will the head angle and therefore the bike geometry.
If you went out and bought a new carbon fork with a lower axel-crown height with
the same rake as your last fork, your head angle would steepen up (i.e. rake would increase)
which would make the bike turn faster.
You could counter-act that by using a fork in with more rake,
but at the same time it would lower your bottom bracket.

If the carbon bike was designed around a certain crown-axel height and you put a taller one on,
it would tilt the whole carbon frame backwards which slackens off the head-angle and seat-angle.
This will make the bike handle/turn slower.
These days it’s getting more difficult to swap out forks
because they’re often integral to the geometry of the frame that it was designed with.
These days there are many crown-heights between fork to fork.