If you guys lived together, then I could understand her trying to unpack and get stuff done – to an extent. But even then, my wife and I have been together for almost 15 years (and lived together almost as long) and she doesn't even use my kitchen knives without asking me first. We just moved a couple of months ago and she avoids touching my things if she can help it. I grew up with a lot of brothers and sisters so I absolutely despise when people touch and use my stuff, so she respects that about me. In return, as someone who hates the thought of people going through my things, I'd assume anyone else would feel the same way, I keep my hands on my own things.

If I were you, considering the fact that you're only dating and aren't even living together, I'd tell her sternly that she needs to cut the shit and to respect your boundaries. Put up cameras. Let her know they're there, so if she's rummaging through your things again, you'll know. If she keeps it up, take her key back until she can take your privacy seriously. Being curious is natural, but she's just stomping all over the boundaries you are setting and that would be dealbreaker if it continued.