From the article, describing the judge’s ruling:

“…and violates due process protections under the U.S. Constitution.”

There’s your federal law.

“Public Use” means the public (i.e., whatever governmental entity doing the taking) owns the property after and eminent-domain taking and does not give it up or resell it to another developer. It would involve facilities everyone is allowed to use (roads, bridges)

“Public purpose,” if they had used it, would have been broader. You could argue that a “public purpose” might include growing the tax base, making the neighborhood “look” nicer, etc. But they didn’t go there.

I see “public use” as stated in the Constitution as more restrictive, and properly so.

So why didn’t the drafters of the Bill of Rights say “public purpose” instead of “public use” if that’s what they meant?

As to the first point, the federal judiciary is empowered to hear cases (a) between citizens of different states, or (b) involving a question arising under federal law. I’m assuming the parties are all Oregonians, and this dispute involves (i) a state statute, held to conflict with (ii) the state constitution. There being no federal question, SCOTUS has no jurisdiction and so would deny cert. In this case, the next step is to appeal to a higher state court or amend the state constitution (a reasonable step), not appeal to SCOTUS.

To the second point: Do you really know what Kelo was about? The dispute was live, to be sure, but in essence the appellants asked the Court to find a right in the Constitution that isn’t clearly there from a textual, originalist or historical basis. The majority who ruled against them reasoned that those who didn’t like it could still appeal to the political process—hardly the hallmarks of an activist Court. And since it wasn’t really clear that “public use” contained the undertones that appellants argued it had, the Kelo majority was far more strict-constructionist than were the dissent, who were willing to interpret meaning that wasn’t clearly there.