Proving a negative is impossible, but right now, the best answers to your questions are:
No, federal statutes do not give the Feds authority to police cities. Federal law gives the Feds power to protect federal property and enforce federal and Oregon law on Federal property.
No, the Feds have not cited any statutes authorizing them to do more than protect federal property.
Since you should not believe me, let me quote Professor Steven Vladeck of the University of Texas. He has impeccable credentials, he wrote about this topic on a well-known and respectedweb site, and his article is referred to by other lawyers writing about Portland.
Here is his answer to the question, **which federal laws are being enforced?"
This is a significant question, and the answer is hardly obvious. Unlike D.C., which is entirely federal territory (and where even “local” law is technically “federal”), Portland is principally subject to the sovereignty of the state of Oregon. There is some federal property in Portland, but not much. And federal law enforcement officers do not generally have the authority (under federal law, anyway) to enforce state laws on nonfederal property.
Some of Acting Secretary Wolf’s statements have referred to vandalism of “courthouses,” including the three federal courthouses in downtown Portland. And there are a handful of other federal buildings in the city.
But this is where the Portland situation starts to look very different from D.C. Protecting a federal courthouse from vandalism is an easy case for the use of federal law enforcement authorities. If, as media reports have suggested, federal officers are patrolling streets a significant distance from federal buildings (and arresting protestors who pose no imminent threat thereto), that would be far murkier.
The fact that he does not cite any federal law answers your question. He didn’t just “end up” not providing cites to federal law. In the article, he explains why he can't cite any relevant federal laws:
- The Feds haven’t cited any statutory authority beyond protecting Federal buildings.
- As he (implicitly) says in the cited section, he can’t think of any statutes they could be enforcing.
- In order to enforce Oregon law off of federal property, Oregon law requires the Feds to do a bunch of stuff they haven’t done.
There may be other experts who have found federal statutes that give the Fed authority to "restore order" in Portland, but I have not found any.
In the rest of the article, Vladeck discusses what authority Feds have to detain or arrest people off of Federal property. (Answer: Not the sort it sounds like they are exercising).
In related article he looks at Federal plans to surveil people who might be threatening monuments, including monuments that are not on Federal property.