When I export animations in blender, only works for the .fbx object that itself attached in unity.

First of all, I'm new at animations and exporting them into Unity. So if you answered in detail, I would be grateful.

I did make some animations on a character and this character holds a stick. I do these animations in separate .blend files but on the same character.

When I imported them in unity, for example, run animation only works for the .fbx object that is attached, but when I try to add the jumping animation on that object in unity, especially the stick animations and general animation don't move properly. Stick doesn't move with it or turn 90 degrees or something. FYI: stick doesn't have any bones only the character has it.

(I realize jumping animation only works properly for the .fbx object that is attached too). So my question is how can I fix it, or where am I doing wrong?

As a solution, I'm thinking of doing the animations as one (running and then jumping), then separating them into two animations (or baking I'm not sure with the term). Then export it. So in one .fbx file, there must be 2 animations embedded. But I don't find how to do it. I'm open to any suggestions.

Thanks