Firstly, I want to acknowledge that this sucks. Your mom is super important for your family, it must feel awful to see her withdraw like that.
I like ~monpetit's thought about patience. Maybe I can give some fuel for empathy here... addiction runs on suffering, and there were clear signs of anxiety at the beginning. It possible she's using her online activity to distract herself from all that, all while drowning it with dopamine. So, we she takes her mind off it, the pain and anxiety rushes back in. Genuine contact requires some silence for us to fill with our thoughts, and that's where pain would come back to her, so it's not too surprising that she'd try to blunt it with multitasking.
I'm not doing so well myself, so I can't structure a post anymore without my thoughts intruding, so I'm stopping here, and I hope it can be helpful.