The test course in the impoverished Hazelwood community is part of a broader plan by Pittsburgh to bring green housing, tech jobs and an autonomous shuttle to the site. That is all at the center of Pittsburgh’s push to transform itself. The public-private effort reflects a surge of similar ambitions elsewhere. Cities across the country, with a nudge from Washington, are trying to remake themselves by taking an expansive view of the role of transportation in their civic lives. They say that they can tackle the era’s big issues — traffic congestion, poverty and climate change — by melding technology with the work of private firms and innovative planners.