Finally I have good news. After literally dozens of phone calls, probably I found a good and safe solution.
There are caravans (trailers/campers) on a separate plot in Őrbottyán, Hungary. I talked to the owner. They are furnished. There is electricity (the heating in the winter is solved by an electric heater), and I can take my Harris's hawk with me. She will be in the caravan with me. The owner allowed it.
Őrbottyán is a town in Pest county, Hungary. The population was 7605 in 2019 (I have not found newer data at the time of the writing of this post).
Tomorrow (on 2022.08.31) I will go there alone to see the caravan, and hopefully to rent it. The rent is 40 000 Hungarian Forint (HUF) per month, which is currently $98.46 USD per month. The security deposit is two months of rent, so 80 000 HUF ($196.91 USD).
So if I will rent it, then I will pay 120 000 HUF ($295.37 USD). Actually I do not have any other choice. The owner is offering these caravans for sale for 500 000 HUF ($1230.71 USD), but currently I do not have that much money. And every other proper caravan have a similar, or even higher price.
Either way, I am happy for this. Even if it expensive. The monthly rent is the half of my pension-like income.
I am visibly happy (or at least not tired) at the moment. Usually I wear my eyeglasses, but this time I took a photo without my eyeglasses.
Have a nice day. All the best. Greetings and much love from Hungary.