My DH became addicted to a silly mobile game and would be glued to it for HOURS every night, if I spoke to him he’d either not process it properly or get fed up with my attempts to converse with him - like he’d decided to regress to being a teenager!
I approached it first as gently as I could, like you experience, he’d improve for a day or two and then back to his old habits! Then I tried logic with him to explain why it bothered me so much, again he agreed he could see it was a problem - then again back to old habits! I got petty and started copying his actions, to show him how it could make a person feel when they were disregarded for a device, he barely noticed because he thought I’d just stopped nagging him...
He made the mistake of telling me this one evening and I BLEW, not suggesting you do the same but once we calmed down we thankfully managed to have a heartfelt talk about the situation. I explained that it felt like I was living with a roommate at best and a bratty teenager at times too, that I couldn’t play second fiddle to a game. Then, why did he feel his phone deserved more attention than me, what drew him in so much? He thought about his answers to these questions for days and finally he explained his reasons as best he could and we hit an impasse for a bit.
It took an argument for me to burn out completely emotionally about the situation and finally just address the situation candidly (I’m not big on arguments, I rarely raise my voice) with him. Basically I said it had to improve otherwise I couldn’t see much more of a future for us (our DD and DS were around 9 months old then).
Also I demanded one “phone free” evening every week to begin with. Where he was welcome to do whatever when I went to bed but not before, he wasn’t overly keen on this though, he managed to do it after a few mishaps with our router that meant he couldn’t access WIFI for a bit (he knows I did this now by the way - as childish as it was for me to do it we actually manage to laugh about it now).
He’s much improved, there are times he will come home from work and immediately out comes the phone, other times he will get to a certain time of evening (after our now 17 month old twins are asleep for the night generally) and immerse himself, then there are spates of time where he’s completely switched on and engaged in the real world. He’s stopped with the petulant teenager bit completely as I also told him every time he behaved that way, I’d be extremely blunt in my replies :’) plus he’s a very doting dad and that keeps him on his toes now the twins can run circles around him lol.