>Do we want to integrate those somehow, or leave it separate?

Using more abstraction has some pro and cons. Pros are that they are forward-compatible and it might be easier to implement yet-unknown changes to the game contents and might or might not lead to more modular and easier to understand code. Cons are that they are usually more time consuming to write and sometimes harder to use.
Especially if it requires the scripter to fully understand the animation system (if they e.g. want to add a new weapon), it might be a turn off.

Soo, I guess that question can't really be answered without a specific pro/con discussion. I am not the biggest fan of the animation stuff/aim manager because it led to hard-to-fix bugs in the past (e.g. being stuck in the drawn-bow-animation). But that also might be an indicator of how challenging it is to write a good system that is robust against all the things that can happen (same as the power system).