It's been a long time since I read Treaty's Law, but I remember feeling that Kirk and Kor got along too easily there, compared to how fiercely they'd clashed on Organia.
I think that's just because we watched the same show, because it's all in there plain as day. Honestly, I find it strange how much distance there is between the popular stereotype of Kirk and the reality in the actual show.
Well, I'm only as far as chapter 5 in Treaty's Law so the dynamic may change a bit. So far it seems consistent with "Errand of Mercy", Kor, like any Klingon, is quick to accuse Kirk and the Federation of attacking the farming colony, but when presented with some actual evidence Kor grudgingly concedes the Federation 'may' not be involved, though he's not convinced it's not some elaborate trick. He also has a grudging respect for Kirk, which he had in "Errand of Mercy" as well.
What I found a bit similar with your story was Kirk's reaction to both Koloth and Kor when they try to get a rise out of him or intimidate him. He doesn't take the bait basically and stoop to their level. Despite his protestations that he's a soldier, he shows he's a very worthy diplomat as well, and one that always knows just the right things to say.
And I think you might have a point that we tend to think of the movie Kirk, partly I guess it's because it's the last thing we see. And of course I think fans sometimes falsely think of the Abramsverse Kirk, who was more rebellious probably because unlike his prime-counterpart, his father was not there in the Abramsverse to help shape him.
You know, as an aside one thing about World Without End is in that book it noted Kirk's father was a member of an Earth return movement (I had thought it was always established Kirk's father was in Starfleet--I thought I saw that in "The Making of Star Trek" or maybe "The World of Star Trek). I was surprised to see that.
Anyway as Kirk aged his views on rules and regulations changed a bit. Now I wouldn't say he actually broke any regulations until TSFS, but later you could argue he 'bent' some rules and obviously was able to argue he maintained the spirit of the regulations (or he would not have remained Captain probably). But yeah, early on I think he was more beholden to the letter of the rules and regulations. I don't think that should be surprising. He became a great captain I think because he understood the intent of regulations--and you would have to know what they are in the first place to understand that.
Now with Treaty's Law the main comparison I see is Kirk's reaction to the Klingons trying to goad him into acting impetuously. That book is obviously much later in Kirk's command so I don't expect to see many points to compare outside that it's another original series book.
But I know I've been thinking of My Brother's Keeper a bit while reading "The Captain's Oath" probably because both stories cover an earlier, lesser covered era of Kirk's career. I expected to compare and contrast it more with Enterprise: The First Adventure, but pretty quickly in I see almost no similarities other than a few very superficial ones (Kirk originally wanting Mitchell as his first officer for instance--though both novels have very differing ways of handling that). But I'm finding the spirit of "The Captain's Oath" to actually feel more like that of My Brother's Keeper instead. Storywise perhaps the "Republic" and "Constitution" books can live in the same universe as "The Captains Oath" (with some specific exceptions), "Enterprise" not so much---that novel did have Mitchell as first officer, Sulu only transferred to helm after Kelso was killed (and was not already an ace helmsman), Uhura was going to come aboard the ship during their refit after WNMHGB and was not already on the ship and the main plot of that book had Kirk's first meeting with Klingons. It's interesting that Friedman went with the idea that I always agreed with (and I think Christopher noted he felt the same way), that the 5 YM started after WNMHGB--even including a couple lines about how the Enterprise was returning to Earth for a refit (to explain the change in appearance of the Enterprise between WNMHGB and The Corbomite Maneuver) as well as crew replacements.
I do think any similarities of the two stories and how they depict a younger Kirk is exactly as Christopher stated, that is how Kirk was depicted in the 1st season, and how Mitchell described Kirk as a "stack of books with legs".