I think the purpose of the word “pre-emptive” is to describe a situation where one side appears to attack first but that side is actually acting to prevent an attack against itself. Consider a less controversial situation: Ukraine launched drones into Russia in order to blow up glide bombs in storage at Russian airbases. I suppose that could be described as a “pre-emptive attack” but I still see it as an act of self-defense.
With regard to your second point: Hezbollah has agency. They weren’t just helplessly carried along by events in Gaza; they chose to get involved. Their choice was predictable, but it was still theirs. One could argue that it was justified (and Hezbollah would certainly argue that it was justified) but justification is a matter of opinion and even if an attack is considered justified, the defender is still, well, defending.