Oh Dear Louise, this is not what you were led to expect.
Could you buy your mum a cup she can use, with her name on? I don`t know if that`s possible, just a thought.
The Home may be fully staffed, but have you asked if any staff are on sick leave, and do they get agency staff in to make up the numbers, for those who are absent.
I would expect all areas to be supervised at all times, but this is just my opinion, and I may be wrong.
Remain observant, and don`t be afraid to speak up, if you have any concerns. It`s early days yet, and you can`t really make an informed judgement in such a short time. If you feel your mum is OK for the moment, it might turn out better.
Take care
Love xx