For the last part they're definitely right, IMO, and german politics must find a way to solve the housing problem in big cities. The government must find a way to break the "migrants take away part of your cake" narrative, and this is only possible by increasing the size of the cake.
In this case, we need to aggressively build (and incentivize to build) more housing. We're doing the opposite at the moment, if the german construction industry is to be believed, which is very very bad. Building a house became insanly expensive in the last 20 years, especially in the areas where it is needed most. Redistribution by moving senior tenants in big cities to suburban or rural areas will not solve the shortage, neither will "just go to rural east germany, there's enough housing".
We have to solve these problems and prevent the formation of zero-sum games where migrants are seen as (external) competitors, stat - it'll be an existential social question and a threat to the country (and the long-term perspective of migrants) if we do not, IMO.