Saw The Post the other day. It's superb. Outstanding. I'll go see it again.
True, it compresses a two-year period of events into what seems to be a short time, and largely ignores Daniel Ellsberg's attempts to get the document exposed.
But The Post is really a movie about Katherine Graham, the first woman publisher of the newspaper.* Screenwriter Liz Hannah had read Graham's 1997 autobiography Personal History, and (at the urging of her boyfriend) written a screenplay based on the book. It's only about the publishing of the Pentagon Papers insofar as it affects Graham. That's why it ignores the critical role played by the New York Times.
* - Graham wasn't the first woman to publish a newspaper in D.C. That would be Eleanor "Cissy" Patterson, grand-daughter of "Chicago Tribune" founder Joseph Medill. An ardent isolationist and conservative who loathed FDR, she published the "Washington Times-Herald" beginning in 1930 and owned it after 1939. She died in 1948, and in 1954 her paper was purchased by the "Washington Post".