What can we do as software devs to help cities absorb the new migrants?

Vote for a government that wants to limit immigration to what can be sensibly "absorbed" and enforce immigration law.

That's not really a software problem.

Refuse to localize interfaces so that people around the world are forced to learn English as much as they were in the '90s. (That's how I learned it. :p)

Help them move to other localities where there is housing and work for them. Perhaps create a job board of more rural opportunities. Make them aware that yes, they can apply for work permits.