Separation anxiety is normal, a part of maturing and yes, it does pass. I’d suggest experimenting to find a routine that your granddaughter responds to.
One granddaughter just needed to be quiet for a while, a sort of grief I think. Another granddaughter went through a phase of being angrily upset when her parents left her. For her the best thing was to wave goodbye and go straight to an activity she loved which varied from a cuddle watching tv to being admired while she ran up and down the garden. It was very much harder for her when they crept away.
Our youngest grandchild is a ‘need to know’ child. So, where is Mummy going, what will she be doing, when will she be back, (eg before lunch, after bath time) and exactly what will I be doing while Mummy isn’t here.
It can take what feels like forever to work out a strategy for each one. Looking back what they needed was and is very individual. Don’t despair, it will definitely pass, a routine of sorts does seem to help it’s just finding the right thing.
France imposing a fine for no-shows at GP surgeries.