Michener had a couple of Navy jobs. During the war he was a "superclerk" (his term) and then an official naval historian. (Klein pg 119) In 1947 he published Tales of the South Pacific, based on his time in the Navy. This was a big hit and became a musical and then a film (South Pacific). After that he did not need to work for the Navy any more, but he kept writing, often closely aligned with the U.S. State Department. (Klein is good on all this.)

It should not be a surprise that the Navy had a lot of historians. One odd thing about the modern "professional" military is that it is not very professional. In most militaries you can have a whole career without a war breaking out. Doctors see patients all the time, teachers teach classes. Military people spend a lot of time preparing for and thinking about something they have never done. Someone (J.H. Hexter?) pointed out that it was exactly when national standing armies were created at the end of the Renaissance that the military became de-professionalized, in some senses. Yes, there were now people who were paid full time to be military officers, but unlike the old mercenaries, who fought all the time (or they would not get paid) the new "professionals" did not do their profession much.

As a result, modern military officers study a lot of history. It is the best way to learn your profession, and they are very big on the lessons of history. I don't know if there are statistics on this, but when officers go to school to get a Master's degree (and bump up their chances of making Major) History is a very common major. A lot of the rest are history buffs. The military loves history and generates a lot of it. The best guide for winning the next war is looking at what worked and did not in the last one.

History is also part of building an institutional culture and, yes, arguing for a bigger budget. Military training almost always involves stories of heroic former soldiers and sailors, and the military generates lots of stories, pictures and analysis for this. I suppose officially the U.S. Navy is entirely focused on protecting our freedoms, and pays no attention to public opinion or lobbying Congress. If you believe that I have a battleship to sell you. The TV series "Victory at Sea" is possible the best example of this sort of public facing military history, and some of what Michener produced would have gone into that project.

Sources

Klein, Christina. Cold War Orientalism: Asia in the Middlebrow Imagination, 1945-1961. 1st ed. University of California Press, 2003.
Mattheisen, Donald J. “Persuasive History: A Critical Comparison of Television’s Victory at Sea and The World at War.” The History Teacher 25, no. 2 (1992): 239–51.

All of the above, mostly. Some background context helps quite a bit to understand this.

Prior to World War II, the Navy is generally terrible at keeping its own history, both in records and what its culture encouraged from its senior officers; one example of the latter is that Spruance felt a single box of notes for his entire career sufficed, where Marshall's official biographer Forrest Pogue went through 3.5 million pages (obviously, not all Marshall's records, but it gives an idea of the importance of history and record keeping difference between the services.) On an institutional level, there's an Office of Naval Records and Library that is one step removed from the General Board in terms of being a complete dead end to someone's career. It mostly publishes old records and is backlogged enough so that instead of working on getting out its World War I archives during the 1930s, it is printing what it has on the Quasi-War with France.

The Navy still isn't thinking much about history after Pearl Harbor, but Samuel Eliot Morison is. In March 1942 he writes FDR - who is not just an admirer of his work but a friend - that he'd like to take on the task of writing up the Navy's actions during the war. He meets with FDR a couple of months later, gets commissioned in the Reserves (a long standing dream of his), receives a letter from Navy Secretary Knox that provides him carte blanche transportation and access to any unit he desires to observe, and in a meeting with Ernest King he gets the cold shoulder for a moment until King realizes this is not any ordinary egghead but one who hopped on a ship for 5 months to write a book he rather liked.

At that point, Morison is essentially a one man history shop, although he shortly brings in several of his former graduate students when he realizes the operations are just too widespread for him to cover them all effectively. While he's not working for his former Harvard thesis advisor for most of the war, in 1944 George Elsey knows full well all the details of D-Day in advance because of his White House Map Room duty, but obviously can't discuss any of it to Morison for security reasons. When he encounters Morison early that year and finds him fretting he'll miss the landings, Elsey suggests Morison mention to FDR that he needs a set of eyes and ears there, which dovetails rather nicely for the former since he wants to get out of Washington for a couple months anyway. FDR and his naval aide Wilson Brown - Elsey's direct boss at the time - approve.

Elsey hops a ride on a troop ship, spends April in London with remarkable access (it's good to have high placed friends recommend you) to places like the British Map Room, and then volunteers for intelligence work in May, which allows him to hop a speedboat with the head of Navy intelligence in the theater on D-Day itself and buzz by the beaches to see how things were going. (Had those two somehow been captured, it would have been catastrophic.) He starts his interviews a few days later, and unsurprisingly, Pogue - then an Army historian assigned to Eisenhower (as a sergeant despite his PhD!) - is already ahead of him traveling with his boss and Bradley when Marshall visits; they cooperate on a large number of oral interviews. Once Elsey returns to London, Clement Attlee grills him during a visit to the British Map Room since he's the first American who he's met who has a good feel for what happened in their sectors. Not a bad bit of temporary duty.

Elsey later spends a number of months back on active duty in 1949 to work on Volume 11 of Morison's 15 volume history, but that was essentially how Morison wrote his magisterial work: with a significant amount of help from observers, and then a whole lot of grunt work by his future grad students going through the drier naval records while he puts everything in perspective and analyzes it.

So what does this have to do with Michener?

Even before Morison begins running his one man (plus) show, as early as 1940 a group of other individuals starts becoming concerned that the Navy is really going to miss the boat on documenting the momentous events taking place. They include some fairly prominent historians like Arthur Schlesinger, but the key person in all of this is a now entirely obscure bureaucrat named Howard Smith. Smith ran the Bureau of the Budget (now OMB) and there's an argument he was probably the single most powerful non-political civil servant in FDR's Administration that didn't have to go through Senate confirmation; he met routinely with FDR to go through spending and was in the middle of almost every budget request from every agency.

Smith had served in the Navy in World War I as a seaman apprentice, which both gave him some familiarity with the culture as well as allowing him access to Bethesda Naval Hospital for treatment while he was running BOB - Howard Bruenn became his cardiologist a year before he did so with FDR, although the results weren't any better as Smith dropped dead at 48 a couple years after the war. But the bigger issue for Smith was that he simply couldn't get a feel for a history of how World War I was run, which mattered tremendously for a lot of analysis, including trying to figure out budget comparisons between the two eras. Morison's bailiwick was to be the Fleet's role in the war, but there was still a need for a broader history on administration, and after a couple of runs at FDR, Smith got him to commit to getting the service heads to record the war on a larger basis in late February 1943.

At that point, the Navy hires another history professor, Robert Albion of Princeton, into the Office of Naval Records as Assistant Director of Naval History and Historian of Naval Administration; the formal change to the Office of Naval History and a full on command structure doesn't take place for another year. But Albion gets authority for hiring 150 naval officers (mostly reservists) to aid him in observing and researching the administrative history, and that's where Michener steps into the picture.

We don't know the exact details of how Michener got the job. He's not an entirely reliable narrator of his life or even the history he wrote about at times despite hiring numerous research assistants, and the Naval Institute never got him to sit down for an oral interview on his service that would have cleared things up. That said, it probably went something like how John Hattendorf transitioned from a line officer to eventually become the King Professor at the Naval War College: he's already on active duty, someone high up liked his work, a history job opened up, and he's interested and his chain thought he'd be a good fit.

So that's how Michener got involved, and yes, he did have a professional historian billet for a couple years at the end of the war. Unlike his superiors, he didn't start off as a recognized historian, but rather cleverly leveraged what he learned into becoming someone generally considered the best paid author on the planet by the time of his death. It wasn't self interest as much as him seeing an opportunity and taking it.

Sources: Administration of the Navy Department in World War II (Furer, 1959), The United States at War (Smith, 1946), An Unplanned Life (Elsey, 2005), FDR's Budgeteer and Manager-in-Chief (Lee, 2021)