If I remember right, the US is also recovering from at least one civil war, and political power is far less centralized than it is in the real world.
Rather than being a long settled question, the pecking order is very much in flux between different agencies, departments, and factions.
So this seems to be something the the modern day pissing matches between the Navy, the Air Force, and the Marines. But far larger in scale, more prone to regional and personal influence, and good old fashion "them that has, gets".
Your comment clarified some things in my mind.
I am not from the US... but even I have an idea how the many military branches are with each other... now we transfer it to this setting, and things get... "funnier".
In this world, the navy has a certain advantage on the political side because of the need to regain the seas, but in a practical sense, they don't do much; their brass will depend on "what ifs" and "possibilities" to wrestle power, but they can never really make tangible results as an organization, but they too can never be dismantled simply because of the enemy they have.
The army, with the civil war, they are hot out of a conflict, in a practical sense, they are the one of the most active and that have true results in these circumstances, they can easily justify their position and budget with the simple fact the country is ablaze and needs military certainty... but they know this is limited... in the grand scheme of things, the true battle is at sea, so even if now they are in their best, it is short lived, and they don't have certainty of how their importance will be even tomorrow.
The air force... well, this one is "complicated"... in a sense, they are at a much better standing than the army, as the type of responsibilities and firepower they have will always have a place, and they certainly have accrued results in the civil war, but just like the army... they know their importance and standing in the big picture is uncertain... at best they would become a supporting branch for the navy, they would keep their independency, but would be focusing all their resources only to play at the navy's needs... at worts, they completely lose autonomy, they are fused to the navy, the very top will be able to keep some power, but we have seen how even in Japan there is a clear difference between the top of the navy brass and everyone else... they would become subordinates, never allowed to be anything more than just a part of the navy... and the air force would never accept tha..
Same for the army, really. Ground troops do have uses, but if they fuck up, they would become the navy's errand boys.