For the "streamer girlfriend" idea, the split screen cellphone idea has a lot of potential depending on how it's utilized. For the "unaware" route, the spicy things could be happening while the BF is at his job doing whatever and thus not paying attention to the cellphone (though we see it of course). Cue some random puzzle mechanic we have to do as gameplay in the meantime. But it also opens up the possibility of using the landscape format main screen to be "at home streams", like sitting in front of her desktop e.g. normal streamers, maybe it's during night when the BF is at home, so rather than watching via cellphone it's watching on the PC. It's mostly normal / cute things but she subtly alludes to her viewers where she'll be the next day for offline meets, e.g. "Yeah I'm looking forward to getting ice cream tomorrow~ There's a place on 92nd street that's just to die for~ Ice cream is best at noon to help you cool down don't you think?~"
If you wanted to keep up the unaware BF bit, only thing I could think of would be she installed a spycam in the BFs house while visiting him to know when he was AFK to flash the viewers for a quick second, but outside of something harebrained like that, I have no idea how you would pull off a lewd stream that a BF would be okay with. Maybe just a "it's just to earn some extra money babe, you're the only I'd let do anything to me~ (lie)". It's a fine line between believability and outright "yeah he doesn't care, go nuts".