Wouldn't sneak attacks conflict with their notion of honour?

That depends. The definition of honor is not universal in Star Trek. Hell, it's not even universal on Earth. According to bushido, a Japanese moral or 'honor' code, if you sneak attack and your opponent is unprepared then that's your opponents fault. Not yours. In the Star Trek Universe, Klingons see things very differently than humans when it comes to honor. A good example would be the TNG episode Ethics where Worf insists on an honorable death despite this horrifying Crusher. Worf also said in DS9 that "In war, nothing is more honorable than victory."

That being said, the Klingons are INCREDIBLY hypocritical when it comes to honor even by their own standards. For examples, look at literally anything to do with Worf and the Klingon High Council. Ezri Dax said "I see a society that is in deep denial about itself. We're talking about a warrior culture that prides itself on maintaining centuries-old traditions of honor and integrity. But in reality, it's willing to accept corruption at the highest levels."

So the Klingons being okay with cloaking boils down to one of two reasons, at least for me. The first option is that they're in denial about the fact that it's dishonorable. The other is that their alien way of looking at Honor just happens to cover cloaking as something that's okay.

A while back I am also thinking of this question, which led me to think about Klingon Honor, which led me to think of the meta origin of Klingon's Honor comes from Samurai's honor... which resemble "face"

From there, I posted the version 1 of how Klingon Honor is a Mistranslation of Face in here: https://startrek.website/post/432321

Version 2 is at reddit: https://www.reddit.com/r/DaystromInstitute/comments/158nyup/klingon_honor_itself_is_a_mistranslation_both_in/. It's far more refined.

TLDR: Klingon doesn't have Honor; they have "face" (due to meta reason of translating "face" to Honor). If you think about face, even cheating is allow; and if you consider cloaking is a type of cheating, then it's not against face. Oh, and a society that focus on face will inevitablely have a high level of corruption dominated by those in power, be it China, Korea, or Klingon.

Winning is the most honorable thing a Klingon can do.

Is it dishonorable for an Owl to strike down a mouse, snatching it before it has any chance to react? I would say no. You could see the tactics of a Klingon Bird of Prey in the same way.

To add to the other comments, honour is a notion that only ever hold among peers. You respect a peer with honor, but a lesser one doesn't deserve honours. A honourable knight is buried with the honours, but a lowly peasant isn't. A knight doesn't have any trouble running down a peasant with its horse. But against a knight he will go down from his horse to fight his honourable peer.

There is an idea of valour in this. When you fight someone of equal value, then resorting to easy tactic doesn't prove your worth against him, you merely used a loser tactic. But against someone you and everyone know is lower, no one care, you're already doing him the honour by merely fighting him. A lower enemy doesn't deserve a honourable fight.

This concept of value and how honour only apply to someone of equal or higher value is important to understand.

Applied to Klingons, they would be stupid to not use a technology like stealth. The question is whether they use it among themselves in fights where honour is a matter.

Oh indeed there are situations where honour doesn't matter. If you need to kill a whole family (for matters of bloodline and right to a crown for example) then you'll deal with honour later.

By killing anyone who says they're dishonorable?

How exactly do the Klingons justify using cloaking ships, a strategy which necessarily involves sneaking up on an enemy and catching them unaware? Wouldn’t sneak attacks conflict with their notion of honour?

As another Klingon points out, the only honour is in victory.

The Klingon code of honour is pretty flexible, and there seem to be a lot of different interpretations of it. Some more dogmatic Klingons, like Worf, might find it dishonourable, and avoid cloaking if they can, but there are other Klingons who are less adherent to tradition, and would freely make use of cloaking as they wished.