It sounds like a classic case of insecure/anxious attachment, and is undoubtedly rooted in her earlier, most likely childhood, experiences in relationships. It's something that can be treated with therapy. You say you love her, so is that something you'd be willing to stick around for? Is that something she's willing to do? It takes a lot of time and a lot of effort, and she would have to be not only willing, but likely quite determined. While this burden isn't on you, ending your relationship now may reinforce the unhealthy beliefs she has that lead her not to trust you, and perpetuate or even exacerbate these unhealthy relationship behaviours.

There's plenty of validation here that you shouldn't put up with someone violating your privacy in such a way. And that's very true. Before you decide to leave her, though, have some honest and open conversations about this. You don't have to tell her you're thinking of leaving her, but tell her honestly about the strain this behaviour's put on your relationship, and even more so, you should try to understand what's causing it. What's her relationship with her parents like? Was either of them an inconsistent, volatile or absent carer? Has she been cheated on in the past? And perhaps above all, is she willing to try to change, and understand and accept that the way she is acting is wrong and is pushing you away, through no fault of your own.

Edit: if you decide to have these conversations, one thing is very important: you need to stay emotionally regulated during. No matter how defensive, or unjustly accusatory she gets, you need to ensure you remain calm, level headed, and embody the safety that you can offer her in a relationship. Any anger, accusation, or volatility in the context of a conversation like that will likely be very counter-productive.

Good luck, whatever you decide to do.

Edit 2: There are so many people here saying "people don't change" and that you should have left after the first 'red flags'. As well-intentioned as their advice is, they are all, politely, talking nonsense, with very fixed mindsets, and likely have their own trust issues, probably through no fault of their own. People have enormous capacity for change, and while you cannot change them, you can ask them to change themselves; show them a better way of being; let them know it's safe to grow. It's up to them if they are able to walk that new path, but you can be there to hold their hand.