I’ll set the ‘virtual signaller’ (!!) comment aside since it’s distracting from the core ethical issue the OP raised.
The issue is not about whether the nanny wants this job - or whether I or you would find sleeping on a blow-up bed acceptable.
The issue is about an employer's responsibilities. The OP is right to feel uncomfortable about a potential imbalance of power and fairness, and to want reassurance that the nanny will be fairly treated.
Saying someone is 'lucky' to have a job because it helps their family is true for many working people globally. But economic necessity does not negate an employer's obligation to provide working conditions that meet basic standards of respect, privacy, and fair compensation.
A paid holiday worker being housed in a non-private common area (like a study) is generally considered sub-standard accommodation for an adult employee, regardless of whether that employee feels grateful for the opportunity.
The fact that the OP is not confident the arrangement is fair is exactly why she is right to feel uneasy. Her unease reflects an ethical obligation to question potential exploitation.
The OP's problem is valid. She is being put in a position of complicity with an arrangement she feels is potentially exploitative, and she is not unreasonable for wanting to avoid that.