okay so it is clearly pathetic that james norrington has resigned his commission/role in the royal navy (an act that would require him to write at least one, possibly two, letters and post them by ship) AND he's still wearing the wig and uniform but i do think as silly as it looks, it's serving a purpose and it's telling us something about james + his relationship with the navy, which is really that James never stops being a Navy man at heart, and doesn't see any of the situation as a way that the navy has failed him even though it absolutely did.
(caveat this is a take on his headspace, because i personally think the british royal navy in those years was Fucked Up, and i often ignore realism for playing with my blorbo.)
norrington resigns not because of fear the admiralty will execute him or fear they won't. he resigns bc he's already lost his honor by failing, but he was set up to fail! he can't SEE it that way, but he was. chasing jack into a hurricane wasn't inherently pride or foolish ambition, it was literally choosing his probable death with honor over his certain death without it. that's the fucked up thing about the navy! it's, per a friend's words, "a society that would never show him mercy!"
when the dauntless goes down, it's because he was in a position where abandoning the chase of jack (esp after already letting him go once) is a crime punishable by death, and then losing the ship and failing to capture jack are also crimes punishable by death. because that's how the navy got men to do insane suicidal things in hopes they'd occasionally be successful-- by indoctrinating them with rules enforced by death. because men are disposable to them!! in his mind, either way, he's already dead. james has heard those regulations read *on a regular basis* over and over for years! he's internalized them!
i think this is where killing jack becomes more than just chasing a pirate bc it's his job, like it was at the end of COTBP. after he lets him go, though, it's not a matter of personal vengeance-- it's just that if he doesn't pursue Jack with everything he has, he's definitely in trouble for letting him go, regardless of personal feeling. but what he's ACTUALLY trying to kill jack for AFTER the sinking of the Dauntless is vengeance on behalf of the ship and lost crew. the moment he loses the dauntless and any lives on it, killing Jack in a form representing the navy (wig and uniform!) is the last honorable thing he can do: finish the job, and make those deaths MEAN something. and bc the story isn't about him it minimizes this a good bit for who it IS about, which is fine, but it does mean that when he stops trying to kill jack and goes with elizabeth, he is essentially choosing elizabeth over duty another time even when he's not actually navy anymore!
the whole reason he's willing to leave her (what fandom sometimes sees as him failing her) is him again trying to recoup from a moment where he picked her over what his honor demanded, per the naval code.
he thinks he can get something from beckett but it's by giving beckett a tool to capture far more pirates than jack alone. and maybe if he tips the scales that much, it'll make up for how he failed
he just doesn't think he deserves to be involved anymore. that's why he's so stunned and then eager for beckett's offer, even with reservations. it's not that he's reconsidering the navy, it's that he never stopped considering it. chasing jack was a job and then killing jack becomes the mechanism by which he can redeem his identity in a system that he still regards as the Good Thing. he thinks he's not worthy of it anymore, not the other way around. the navy has made suicide missions (damned if you don't give chase, damned if you do) the only way to avoid execution or dishonorable discharge with pay and prize money reclaimed, but they did so in a way that made men like James feel like THEY were the ones failing short of an ideal, unable to truly face how wildly unrealistic the ideal is, because they can hold up the few survivors of such efforts as Wonderful Patriotic Heroes. this is not a situation where James has been broken and decided that the Navy and it's culture are harmful, dangerous things, where he's disillusioned. this is a situation where James still regards the Navy and its expectations as THE ideal, and part of his despair is that he's fallen short of it.
i think in cotbp, Gov Swann's words at the end are potentially a catalyst for james to question blind justice and loyalty to the navy, but that's like, the barest hint of an exception given as an excuse, and not something that's shaking his foundations yet. i think this is why "james is cool with being a pirate" takes rarely work for me, actually. if a story puts in the work to deconstruct his entire prior life and beliefs so he is ruined and broken down by that and has to start over, i can buy it. but i think people see his low point in tortuga as a situation in which he feels the navy has betrayed him and he's reconsidering pirates, and it's not. his low point is there because he still thinks the navy is Right and Good. he resigned his office to hunt jack before they could execute him for failure-- a thing that would be justice, to him-- in hopes that killing jack would absolve him of embarrassing the Navy that he was a symbol of, and restore the Navy's honor that he muddied. he says jack cost him his commission and his life because he holds jack responsible for existing as a pirate, not because jack was responsible for the hurricane or the ship.
and then! he stops trying to kill jack! for elizabeth! and that lasts long enough for him to find a way to HELP THE NAVY AGAIN. he's willing to settle for being a privateer but he's so far from being a pirate at that point in his life. he still loves and fears and breathes the navy and the navy right to govern the way they do-- even at his lowest in tortuga, he's there BECAUSE he's clinging to the Navy's justice as a good thing, not because he's thrown the navy over. is there pride involved? of course. but it's far, far more complicated than personal pride alone, or even primarily, and very much wrapped up in what happens when someone's identity is rooted in a system intended to manipulate them into sacrifice.