Well yeah, but there are lots of situations where your intent with a threat matters. Saying “I’m gonna kill you!” to your brother when he throws a water balloon at you is rightfully not considered a legal threat. Saying “I finally bought a gun and I’m gonna kill you!” might fall into either category for me personally, depending on whether they had actually recently bought a gun.
I’m really not trying to be difficult here and I do absolutely see how this could be ruled a legitimate threat, I just don’t think it’s 100%. I’m leaning towards 80% (assuming she didn’t actually recently get a gun), given that this is Florida.
Regarding the diary, I was actually thinking of that exact scenario, with the stipulation that the diary is locked. I would be interested in whether that aspect of the law has been tested yet, but it’s probably not that common.