We have way more than enough housing. The problem is they're wildly unaffordable or hoarded by people buying vacation homes or investment properties. Some are also from inheritance that they just refuse to get rid of cause they'd lose money or some nonsense.

Maybe but we already know we need more housing, no need to spend a bunch of money to find that out, especially if that money can be spent on actually building housing. There are plenty of other stats and signals we can use to determine what to produce which don't require bringing inflation into the mix that can cut into peoples savings.

Also, if someone earns 1000 and you earn 500 before an UBI of 500, they earn 2x as much as you before and 1.5x after.

Yes but your ability to outbid that other person stays the same. In a market system your access to limited goods and services is determined by your ability to outbid others to gain those goods and services.

Take housing for example, say I can spend $500 on housing for a shitty apartment and another person can spend $1,000 on housing for a good apartment, and there's another unhoused person who can't afford any housing.

Now give each of these people $500, like you said the relative gap has shrinked but the place in the hierarchy stays the same. The person with the good apartment will bid up prices to keep me from moving into their unit, and I'd be forced to bid up for my unit to make sure the unhoused person doesn't get it. The distribution of housing would stay the same, assuming no new housing gets built, and all the money just goes to the landlord.