You already answered your own question: the poll is talking about missing middle housing- stuff like triplexes and low rise apartment buildings. I also pointed that out. I never brought up social housing until you did.
Homelessness can be addressed without social housing if you want to. It turns out that the biggest driver of homelessness is a lack of housing. Simply allowing the construction of much more market rate housing increases the vanacy rate, which drives down rents and homelessness: https://www.sightline.org/2022/03/16/homelessness-is-a-housing-problem/
So I have no idea why you are going on about social housing.
I have used all the statistics and polls in their original context. A lot of people, including in New York City, support allowing the construction of more housing: https://s3.us-east-1.amazonaws.com/rpa-org/pdfs/RPA-NYC-Issues-Survey-Topline-F0...
New York City has a low vanacy rate. And so on.
The Sightline poll literally shows that "A poll conducted this January shows over two-thirds of polled Washington voters support a statewide zoning law to construct more missing middle housing."
It is talking about market rate new housing, not social housing. Your original post on this game was about market rate housing, judging by the mention of corporations on it, and I responded with points about market rate housing. I don't know why you keep bringing up social housing and crime when I was talking about market rate housing.
The majority of NIMBYism I've seen is resisting new market rate housing. So, presumably people do care about duplexes.