So myself and DP, together 8 years, lived together for 5.
Both always wfh and now with covid have spent a lot of this last year in each other's company.
A few weeks ago in a silly argument DP suddenly accused me of cheating on him. This surprised me because a) I'm not and b) even before lockdown my social life was very low key and any socializing I did he was with me 90% of the time. His accusation was also just very nebulous and not about a specific person/time or anything like that.
The next day he apologized for what he said and claimed to not mean it. He then kept bringing it up "as a joke" until I told him it was hurtful and if he had an accusation to come out and say it or to pack it in. He apologized again and agreed.
Since then he has gone out of his way to look at my phone three times that I've seen. I use my phone for work/banking and its always left lying around. He sometimes uses my phone if his is dead and every time I tell him the password. It's a password/set of 4 numbers he could easily remember but seems not to and needs reminding each time. I get the odd message from friends and some social media alerts (twitter). All above board chatting. I am a very boring person 
I can't emphasize enough that this is a tiny trickle of messages, not loads, not that this is the point. Basically I'm not precious/protective about it at all.
The first time he did it he was holding my phone for me while I sorted something and I turned around to see him scrolling through the alerts/messages. It wasn't so much that he did this but he seemed so intent and serious as he did it, and he'd waited until I was turned away.
The second time I dropped my phone down the side of the sofa while on my laptop. He came across the room and insisted on picking it up. In the process he blatantly checked the phone and the computer screen. I don't mean glancing.
I was logged into my bank on the laptop and my phone to check and move my savings around. Dull, dull, dull. I gave him a bit of a disappointed look and he cracked some joke about oh these men send you money now do they.
I told him to do one.
Third time was just now. He needed to use my phone to make a call. He walks out of the room as the call ends, full minute passes and he walks back in blatantly still scrolling through these boring twitter notifications on there. He was really upbeat afterwards, like he was relieved.
Also, around a week ago we got a takeaway from deliveroo, ordered online. When the status changed to being delivered I went downstairs to receive the delivery. When I came back up, (had to wait a few minutes), the deliveroo tab had been closed, the tab with my twitter was open (I have around 40 tabs open all day everyday and spend very little time on twitter). Dp was also behaving very strangely. I asked him in a joking way if he was messing around on my twitter and he told me that my computer made a weird noise and shut itself down. I pointed out that it was not shut down. It's an ancient model, take ages to start up and besides all my programs (I work as an illustrator) were open and as I left them. He is a terrible liar and this was just obviously not true. I let it go but this bothered me mainly because I write fiction as a hobby and a way to to mange anxiety and he knows that I don't ever want anyone to read any of it unless its finished and also something I wanted anyone else to read.
I just felt really invaded, like he had read my diary or something. He kept coming up to me and hugging me after that and making some odd comments about was I ok, etc. My impression was that he'd read something about depression in the tab where I do my writing. Maybe he didn't but that's what I am thinking now.
Just to be clear if he wanted to use my computer to check something then that would be fine. I don't expect him to root around through things though.
Just before he started with this behaviour he told me that his last serious gf had cheated on him, I never knew this. She also did some unpleasant things like bringing the new bloke round to his house after she left him (for this other guy) and they basically let themselves in. She met the guy online and that's how they built up to her leaving to be with him.
Obviously lockdown has taken a toll on everyone's mental health and this seems to be an insecurity of his that has risen up but my mental health has taken a battering too and while I don't really give a fuck about the phone, waiting until I'm out of the room and then checking through my laptop/reading what is basically a diary and lying about it is not on. I don't know for sure that he did that but he blatantly lied about why the Deliveroo tab was closed and the Twitter one was open.
I'm just tired and I don't need a new problem right now. Thanks for listening.