There are so many decent families looking for au pairs, run a mile from this one.
I had au pairs when I was young, and into my early teens as my mum wanted someone in the house when I got home, even though I didn't need looking after by then!
They were always treated very much as as part of our family and we're still in touch with most of them. They had a lovely room and my mum spent lots of time making sure they had all the information they needed about how to find English classes, how to navigate living in London, what things they could do locally etc. (This was pre-internet so very much needed!).
We sometimes got other au pairs who were friends with ours, hanging out at our house, seeking advice on being treated terribly by families and my mum counselling them what to do! (Run a mile, basically!) It was a real eye opener as to how some families treat au pairs like old-school servants.
One lovely young told us how the family treated her terribly in myriad ways then told her she must smile and how she should greet them when she saw them! The brass cheek of them!
Ditch this family, you owe them nothing.
It may also be worth reflecting that as girls and women, we're socialised into putting others first, and this isn't a good thing! Although it can be hard to fight.
This, for example I want to give them a chance and make sure I’m worth having around is giving them too much. Give yourself a good chance for your au pair experience to be a success instead, by finding a much nicer family who actually deserve someone as nice as you. Advocate for yourself, not for these people who don't think you need more than a tiny, cold room!