I admittedly haven't done well at rebuilding trust, having a few months ago secretly gone through her phone (I didn't find anything). I didn't come clean and admit what I'd done, I sort of threw it at her in an argument and she was understandably upset.
What could you have done better to rebuild her trust in you? Why did you feel the need to go through her phone? Was she more upset about you feeling the need to go through it, or was she upset because she was hiding something?
My H and I have open device policies, where we have each other's passwords, access to everything, and ongoing permission to look whenever we want to. Neither of us get upset when the other looks because we usually do not have anything to hide. We had this setup prior to the infidelity issues as well (and honestly one of the things that confirmed something was going on with me when I was cheating was the panic I displayed a couple mornings when I woke up and couldn't find my phone.) I think that this arrangement works well. If we feel the need to go through the devices, we often talk about why that is and try to work on the root cause.
Arguments happen, I keep getting accused of lying even when I'm not,
What are you arguing about? Are you looking for ways to reassure her that you're not lying in a way that is comforting, or are you reacting angrily/defensively at the accusations? Your actions damaged the trust; the former conveys that you're sorry about it, that you care about her feelings, and that you want to rebuild that trust. The latter conveys that a desire to "move on already" from her distrust, like it's unreasonable for her to have it, which can trigger memories of being lied to or gaslit when the infidelity was going on, and worsen the trust issues.
I think a good template to use is a) apologize that you caused these feelings of distrust in her, b) attempt to propose something that would help her feel better or offer whatever proof you can, and c) ask her if there's anything else she needs or that you can do to help her feel better. This might help her not flood so badly that she threatens divorce...
Though I think you are within reason to request that if reconciliation is still on the table that she does not make empty threats of divorce in the heat of the moment. Recovery and reconciliation are hard for both parties; it's extremely demotivating for either to think they are expending all this energy and effort into a marriage that the other doesn't even want. Empty threats of ending things just shoot the reconciliation process in the foot.
The "D word" is not something we use lightly in my marriage, even if we are at each other's throats. Even as rough as things are right now, we are still both focused on repair. D is the last thing we want and we would never threaten it without seriously considering it. Big no-no.
I also think any discussion of removing access to accounts needs to be done when both of you are calm, not when emotions are high, because if she is already triggering and trying to self-soothe by looking through your stuff, leveraging her D threats to hurry her up or to rescind that access just makes you look guilty (even if you're not) and worsens her trigger... So what if people start messaging you? Respond to them or don't, whichever is appropriate and suits your goals.