This is quite standard these days, some people have cameras throughout the house.
Let her watch her daughter remotely, if that makes her comfortable for her daughter to stay overnight, then that's what you do.
You have a busy life but remember these are opportunities for you to spend quality time with the grandchild. If you view it as putting yourself out or doing a favour for your daughter then that makes it a transaction and feels like strings attached.
If this were not a normal behaviour, ie: she didn't use the camera at home, I'd say you were right to feel off about it but actually, this is normal life for her.
To have a good relationship you need to respect her rules, if you don't you will be seen as untrustworthy because she makes them as the parent.
Some parents are anxious, been there, still doing that but you can still be a great parent that doesn't suffocate children... My AC are pretty confident and resilient
Also you know, some children like the comfort of this, mum is there even if she isn't. I have a very tired little boy who brings himself down the stairs if I haven't gone up and given him a hug and turned his light off when he is ready to sleep.
Don't worry about it, enjoy time with your granddaughter, it's a new digital age