Feels as if President Donald Trump just got a political post-halftime push.

Midway into a (first?) term marked by battles with media, the president’s favorite enemy has handed him — and all who clamor about “fake news” — some added motivation.

And, more broadly, created yet another test of media credibility.

There was the BuzzFeed News story late last week saying Trump had told his lawyer, Michael Cohen, to lie to Congress, a potentially impeachable offense.

But the story was labeled “not accurate” by the office of special counsel Robert Mueller, after much of cable TV news obsessively pushed it for a full news cycle as an end-of-Trump development.

Then came a widely disseminated story and viral video of MAGA-hatted Kentucky Catholic high school kids appearing to mock an American Indian at a D.C. rally over the weekend.

But additional video emerged that seemed to vindicate the kids, just after significant national reaction suggested fault for their insensitivity rested squarely with the president.

Both instances underscore a major media (and social media) problem: rushing to judgment regardless of verification.

Trump gloried in the gifts he was given.

The BuzzFeed story was “a disgrace,” he said. “It’s going to take a long time for the mainstream media to recover its credibility.”

And he said the Kentucky kids were “smeared by media.”

Thing is, all media took a hit.

“It’s unfortunate and frustrating, but we have such an overheated media environment now, and we’ve all been lowered by cable TV programming and its pressure to have something to say all the time as it mixes commentary and news. … It hurts everybody in the news business.”

That’s from Penn State communications professor Patrick Plaisance, whose focus is media ethics.

Plaisance spent 15 years as a newspaperman in Florida, Virginia, and New Jersey (the Trentonian). He said that in the case of BuzzFeed, the fact that no other news outlet could match the story presents problems.

“We need to rethink how we see political news. Maybe it’s not worth our time if we haven’t verified it ourselves,” he said.

BuzzFeed News is no fly-by-night shop. It was a Pulitzer finalist last year for international reporting. And, in the spirit of withholding judgment, its Cohen story, which it is standing by, might yet prove to be on point, if wrong in some details.

Still, Plaisance is right regarding other media. If you can’t match it, don’t rehash it.

Brendan Nyhan of the University of Michigan’s Gerald R. Ford School of Public Policy, who specializes in politics and media and is a contributor to “The Upshot” at the New York Times, agrees.

He, too, sees problems in rushing the news: “It’s fair to say unverified claims of whatever sort are too often amplified too far, too fast. … People who care about the media’s role in a democracy should be concerned about breaking news without time to assess its veracity.”

Two years ago this month, I wrote that Trump took office fighting with the media over the size of his inauguration crowd. It was an inauspicious start that set the stage for a tug-of-war over America’s trust.

Two years later, that war goes on, and one could argue no one’s winning.

Yes — despite instances, such as the BuzzFeed flap and MAGA kids — national surveys show trust in media growing since Trump took office.

But Gallup’s latest poll on media, released last October, shows only 45 percent of Americans have a great deal or fair amount of trust in mass media.

That’s a big improvement from an all-time low of 32 percent in 2016. But Gallup polling puts Trump’s approval rating last October at 44 percent, basically tied with media.

At the start of this month, Trump was at 37 percent. Unclear where media is.

What is clear is that the war continues at a time when media’s most valuable aspects, serving as watchdog and holding power accountable, are especially needed.

It won’t surprise you that I believe journalism — real journalism, measured and verifiable, whose job it is to get the public as close to the truth as possible — is more important than any politician (or president), whose job it is to push policies and win elections.

Just don’t confuse all mass media or social media with real journalism. Because even if the latter is sometimes flawed, it is almost never fake.