I'm mostly happy with my relationship with my phone. Part of it is setting things up so it's not front and center in my life (disabling and/or silencing most notifications and only allowing calls and messaging apps to vibrate) and not really having a lot of "interesting" things on it that are easy to slide into and hard to pull out of (social media, which I've been fully off of for 4 or 5 years, and addictive games).
But yes, there's a component of self-control, too. I could easily pull out my phone and start scrolling Google News, reading alarmist headlines and getting myself wrapped up in them. And sometimes that does happen. But for the most part I just... realize I don't like how I feel when I do it, so I don't do it[0]. If I'm waiting around for something (transit, waiting room, etc.), I'll first see if there's anything else to occupy myself with, even if it's just people-watching or enjoying being outside. If I'm not feeling it, then sure, I might take out my phone and read something in the Kindle app, open messaging apps to find someone to chat with, open the browser and check out HN or a news site I enjoy, etc. And that's fine. The key thing is that I've looked at the world around me and actively decided that I'd rather read something on my phone to pass the time.
I don't think you need to develop this self-control through shame. Think about why you want to stop being on your phone so much. Frame that with respect to how you feel when you're using it. Not the results of the dopamine hits, but how you actually feel. Do you dislike the mindless aspects? Do you dislike all the inflammatory, outrage-inducing stuff that the algorithms throw at you? When you finally do put the phone away, do you lament the time you wasted, and think of other, more productive/useful/joyful things you could have been doing? Don't be ashamed, but do let the actual feelings associated with your phone use wash over you, and if you don't like them, start committing to doing things that don't make you feel that way. I'm not saying it's going to be easy for everyone to do that, but I think it's necessary.
If you can't develop self-control that way, try to leave the phone at home sometimes. Not in the "amputating it with a hacksaw" sense, but in short, easy, low-stakes situation. When you go into your kitchen to have lunch, leave your phone behind. It'll still be there, a couple rooms away, and you can pick it up again after you finish eating. Next try leaving the house without it. Got outside for a 20-minute walk around your neighborhood, without your phone. Next leave the house for longer without it. You know how to get to the grocery store. You've done it a hundred times and don't need your GPS. Write or print your grocery list on a piece of paper, and leave the phone at home. You'll be home in an hour or so, and then you get it back. Realize that there are actually a lot of situations in our lives where we can do this, and give it a try.
I think I'm lucky that I was a child of the 80s and 90s. I grew up without the internet until my teens (and then it was just intermittent dial-up until college), and without a smartphone until I was nearly 30. I got to see the evolution of a lot of this technology, and I believe that allows me to be more mindful about what I do and don't use. I know plenty of zoomers and younger millennials who have had always-on internet in their pockets for most of their lives, certainly for the entirety of their adult lives. It's all they know. And I think it's becoming harder and harder for today's parents to limit or deny screen time, as there can be severe social consequences for the children when that happens.
[0] This is how I got myself off social media. I examined how it made me felt, committed to a month with no access to it, examined how that felt, and realized I was so unhappy scrolling my feeds all the time. I still have the accounts open, but I've deleted all the apps from my phone, signed out on desktop, and disabled all the email notifications they send.