AfD support is much higher outside big cities, especially in rural east Germany where there's enough housing.

https://www.zeit.de/wirtschaft/2021-02/mietpreise-deutschlan... claims that the lowest rents in 2021 were in Elsterberg in Saxony.

https://interaktiv.tagesspiegel.de/lab/bundestagswahl-2021-k... shows the AfD getting 25.7% of the vote in Elsterberg during the 2021 federal election, ahead of all other parties.

You may worry about the cost of housing in big cities, but I doubt the typical AfD voter does.