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Basic plot is a galactic war between two factions, but that's backstory not the focus. The protagonist's side is human, I don't recall the enemy as they weren't really the focus of the story as I remember it. They might have been human as well.

The story starts with the protagonist having already been captured and is being sent to the prison planet, which is only populated by prisoners of war. His identity is kept vague to the reader.
He's taken in by the existing prisoners, who have an established hierarchy based on their military rank before capture.
I have a memory of forests and maybe tree houses, with that sort of 'wood based' technology, if you see what I mean. But it's vague and I could be mixing this up with another story.
I think he is given a bit of a hard time initially, and the prisoners have essentially forgotten about the war.
Then at the end of an early chapter it's revealed as a 'twist' that he's actually an Admiral (or some other equally high rank) and is in fact now the highest ranking prisoner on the planet and therefore assumes command. This twist is the thing that stands out most in my mind.
He then knocks the prisoners into shape and I think orchestrates an escape and return to the war.
I remember it as being reminiscent of WW2 PoW stories like Colditz, but it was a long time ago.

Pretty sure I read this as a paperback in the eighties, or maybe early nineties, and at the time I was reading a lot of second hand books that were written in the 60s and 70s. For the longest time I thought it was a Harry Harrison novel, as I read a lot of his work at that time, but having reviewed his work I can't find it. Might be a short story though as I haven't gone through all the possible collections.

Some additional thoughts. In the early stages where his identity is being kept from the reader, I think the character was quite despondent about being captured. After the reveal I think the dynamic was him being a great military leader, and getting the prisoners to remember they are soldiers and fight back lifts him out of his despondency.

When I talk about wood based tech, I basically mean boy scout type stuff as they don't have proper technology or metal in the prison. Hence tree houses, huts, or something like that.

Possibly The Escape Orbit by James White (1965)

Here is a cover from the original 1965 Paperback

And the 1983 reissue which I remember

Basic plot is a galactic war between two factions

The War is between Humans and chlorine-breathing Bugs.

I have a memory of forests and maybe tree houses, with that sort of 'wood based' technology, if you see what I mean.

The prisoners are given just enough equipment to establish a primitive agrarian way of life

the prisoners have essentially forgotten about the war.

The war has lasted almost a century, and the society on the planet has devolved into 2 factions. "The Civilians" - who have been there a long time and want to forget about the war and move on with colonizing the planet. And "The Committee" - who believes it is the duty of every military person to plot escape. They have been working on a "plan" for many many years, but it just never seemed to be the right time to activate it.

Then at the end of an early chapter it's revealed as a 'twist' that he's actually an Admiral (or some other equally high rank)

The Protagonist is not just another captain, as the other prisoners assumed, but rather a Sector Marshal.

This reminds me of Revenge of the Damned, one of the Sten series by Alan Cole and Chris Bunch. The story starts in a POW camp on a prison world. The enemy are the Tahn, human but not part of the Empire the Sten serves. Sten was recorded as a prisoner under another name ("Horace" something, don't recall the last name) because his friend Alex had switched his dog tags as their ship lost power and and enemy started to pour in through the many rents in the hull (end of the previous book, Fleet of the Damned). These stories were heavily styled after WWII fictionalizations -- Fleet after the loss of the Philippines near the beginning of the war, and Fate after the German prison camp system, specifically harking back to Colditz.

You have the rest of it -- Sten winds up, not commanding the prisoners in the Colditz analog, but as "Big X", in charge of coordinating all escape attempts, then (because of his background as a spy, as well as all prisoners having been trained in how to be bad prisoners) winds up running a lot of operations from inside the prison before the final escape. These books (nine in the series, as I recall -- don't have my bookshelf where I can see it at the moment) came out in the early to late 1980s, and are well worth rereading (still available in ebook form, at least).