It sounds more like they're using more fundamental movements than what you're describing, not running animation+shot animation but more like:

Both reloading a particular weapon and mantling over a walk require you to lift your arms, so the root movement of lifting your arm to reload an LMG is the same one used to grab a ledge overhead, etc.

Basically they're just categorizing movements based on use case and direction so they can string those individual movements into different and unique patterns for individual actions.

Pressing an elevator button uses the same arm movement as opening a door, which uses the same wrist rotation movement as turning the key in a car, etc. So they just break down individual movements in the same way an LLM breaks down a voice into phonetics to string new words together.