Interesting that those look at quartiles and quintiles. The top 20% isn't necessarily "rich," the bottom of that bracket is barely able to afford homes today. The homelessness spike is not driven by the poorest getting relative wage increases faster than the middle class, which is the story presented in your sources. The homelessness spike is caused by 50 years of working class incomes growing slower than housing costs.
Inflation hits lower income brackets harder. Wages in the lower brackets are not keeping up with inflation. The continuing spike in homelessness is a direct result of wage stagnation in the lower and middle classes. The notion that lifting people out of poverty will drive inflation is farcical and perpetuates the growing rates of homelessness and poverty. Think for yourself, "idk" isn't an excuse.
https://archive.ph/A9OTx