No, she started staring at her phone eventually later on while I was sitting down there.
I started looking at the tablet when the convo with her fizzled out (I would argue that I tried to talk with her, she didn't really respond in an engaging way to make me want to continue talking with her, I had brain fog, and a proper convo didn't really take off). She was also looking at a netlfix program on her smartphone at the time. I did attempt to engage in a convo by asking what she was looking at (ie Netflix show "Love is Blind"), and asked about how her lunch was, which she cooked up in a microwave oven and probably made at home and warmed up there on a container.
The opener when I approached her was simply to greet her and how her day was, and when she asked about my lunch, I asked if I could sit next to her for the lunch. I've approached her at least once or twice before, where I ate my lunch at another table, but on my way to the desk, I'd stop at her table, say hi with her, and whenever she asked about my lunch, it had always been consumed at another table away from her. Eventually, especially after seeing another guy sit next to her, I finally tried to eat my lunch next to her and see how that would be like since she had always inquired of me before if I had already ate my lunch....it sort of felt like she would have wanted me to eat my lunch together with her rather approach her after I had eaten away from her, just to have like a 10 sec chat, and move on to my desk.
It felt on some level that she wanted me to have lunch with her rather than consume my food away elsewhere and then approach her for a brief chit-chat, and I kinda wanted to do that too if there was any hint she wanted that.