Is this behaviour normal?

I (27F) was seeing a guy (28M) for about 6 months. I've already left him because he was verbally, emotionally and physically abusive. I know leaving was the right decision, but there's one thing I can't get out of my head.

He was obsessed with going through my phone. If he got access to it, he'd go through my WhatsApp, Instagram, all social media messages with friends—basically everything. A lot of the time, he'd do this while I was asleep, so I'd wake up to him having read through my private conversations. At one point, he even exported my WhatsApp chats with my friends so he could read them later. I never experienced anything like this before.

The weird part is that he once told me his ex used to go through his phone and that he absolutely hated it. Yet he did the exact same thing to me, except it felt even more extreme.

This has made me question what is actually normal in relationships. Is it common for partners to go through each other's phones like this?