OP, you need a new nanny. Just google a proper agency to find one.
My nanny does 4 hours per day with no breaks. Obviously she eats and goes to the bathroom when she can just like I would - she just treats the place as her own for the hours she's here.
The agency I went through specifically forbids employees to mess around on their phones which is an indicator that your nanny is being unprofessional. I'm sure you can find a similar agency.
My nanny sends me pictures of my little ones when I'm out and I prefer she has her phone nearby and checks it in case I need to tell her something.
If the babies are asleep she reads her phone or plays games on there but why shouldn't she? The second they are awake she is playing with them, feeding, bathing, reading, talking etc. I expect this of her because that is what I would do myself if I could. I hate not being able to be with my babies and I pay her well to do all the things I feel guilty about being unable to do myself.
If there was an emergency for her of course she should know so she should check if she gets a phone call or text, but unless urgent I wouldn't expect her to be on the phone.
Oh she also looks up interesting things to tell the older one about, or checks things to do with the babies like when they're due a wonder week/growth spurt.
I think phones are very useful. They are a part of modern life and they make things fast, interesting and convenient. If their use impacted a child negatively, like indicating to them that they are not as interesting as what you're reading, then thr phone should be put aside.
The nanny in question is taking the piss. I don't think a chat will cut it in this situation. She works only 3/4 of the time she's there and doesn't even do it properly for those tiny 45 minute segments. She seriously can't focus on your child for 45 minutes? Go hire a professional.