The whole frame deal got me thinking about a possible root cause and after I successfully imported my fbx animation, it makes some kind of sense. In Blender 3.3 LTS (It might work in other versions) I had to select the armature, make sure the right animation was loaded, zoom as close as possible in the timeline until I could see the scale at 1 frame per line and move the keyframes of the animation until it snaps to the nearest frame. Lucky for me I had a 60 frame animation but it worked. Also, the original animation had a frame poking outside the frame range. Could that be a cause? As far as I know if every frame is exactly lined at the frame mark, and not in between two marks, it would fix it.