> Obviously the US can afford housing the homeless. I just don’t understand how a judge can just decide to spend a billion dollars.

The judge didn’t decide to spend a billion dollars. The judge ordered the city to put $1 billion dollars the mayor had pledged to the cause of homelessness in escrow. The actions ordered by the court may cost more or less than $1 billion.

The courts have broad authority to order government or other parties to take action to remediate (or cease exacerbating) unlawful harms they have caused; and $1 billion isn’t anywhere near the maximum that it has cost the subject of such an order to comply.