> What’s an example that you believe highlights NYTimes moving rightward?

Look at their coverage of Alexandria Ocasio-Cortez's response to a question about Taiwan versus Trump's response to a question about Taiwan. In the first case, their quote included all of the um's and other similar pauses in answering the question. In the second case, their quote of Trump cleaned up all of those artifacts. The end result is that it looks like AOC is flailing to come up with an answer while Trump has a clean, polished answer. But if you compare the actual audio clips of both answers, Trump's answer is the one that involves far more flailing to come up with a response.

There is a general pattern in the more subtle aspects of presentation and framing that generally excuse the behaviors of right-wing politicians compared to the same actions being done by a left-wing politician.