Nothing much for housing besides the general housing assistance schemes.
Socialism is a giant umbrella of political philosophy.
More accurate term would be 'regulated calitalism' or a subtype of socialism called 'democratic socialism'. Both of which coexist alongside of capitalism just fine.
It's always extremes with people on both sides because most people from either side don't understand what they're talking about.
Now, you say '[democratic socialism can] ... coexist alongside of capitalism just fine'. It seems much more likely that it is actually normal socialism with the names of things changed. The issue with socialism is that it vests decision making power with government (topically, the thing that is shut down in America at the moment, showing how reliable governments are).
Decision making power can really only be vested with one person. That person might be a capitalist, a politician, a bureaucrat, a worker or a customer. The only system we know reliably works is a capitalist/customer hybrid where major decisions are split between the two (capitalist gets the how, customers the what), with very mild influence from the rest (eg, safety and environmental regulation, wage negotiations with workers).
When the government starts making and enforcing allocation decisions like 'everyone must be paid this', 'everyone gets a house' or 'everyone should get medical attention', it doesn't matter what you call it - wealth will be destroyed. If the wealth destruction exceeds the ability of the economy to create wealth, there will be mass suffering. It doesn't matter what it is called.
Nothing you said is a fact. Everything you said is 100% opinion.
Everyone's entitled to their opinions.