@Bjørn-and-Vibeke0 i am sorry for your unpleasant experience
If your bed is now repaired then maybe it would be better to stay at this accomodation and spare yourself of a research and relocation to another place.
If your bed is still broken then you can contact Airbnb and ask for more refund, cancellation and relocation.... or you can buy a hammer and repare it by yourself in few minutes .
I would probably take their offer and repair it by myself . But I like quick and stresfree solutions ... and I am ok with tools 😄