There's a scene with Worf and Kurn in a pub during the civil war that is more Lower Decks than Lower Decks. It's like the background extras were lifted straight out Pirates of Penzance.
I can see where the Klingon empire didn't survive. The destruction of Romulus seems to be a larger event than one supernova/system (because otherwise, its barely believable that the major power that was the least damaged by the dominion war would lose the ability to survive losing a single star system as in ST'09). If the destruction was wider (lets say trilithium stores (with weapons like in ST:Generations) being detonated, causing quickening live-cycles/mass supernovas across the beta quadrant), it could see the Klingon's bearing the brunt of the damage. Its inconceivable that the Federation/Klingon alliance was intact while starfleet built an armada for romulan civilian rescue. Next is the burn. ST:TUC showed that Klingons are willing to do heavy mining extremely close to population centers while the Federation (in what little industry is shown) keeps its planetary industrial centers away from class M planets (Mars, Jupiter). It's quite possible that the dilithium mining and use on a planetary scale caused destruction of major population centers, transforming planets into, best case, what was seen in Discovery S3E02
Well, it's unlikely that the Romulan supernova would only affect the Romulan solar system. But setting that aside -- is it really so hard to imagine that the loss of the imperial center would cause an empire to splinter? It's not like this is a decentralized polity; it's a literal empire. I don't agree with that at all, especially with Martok as Chancellor. I could easily see the Klingons deciding that there was no honor in allowing billions of innocent civilians to die. For all we know, the Klingons might have considered the Federation decision to withdraw aid to be deeply dishonorable. I don't think it's likely a supernova in the heart of Romulan space would affect the Qo'noS system.
The Klingons as we know them no longer exist. The entire species migrated to the Delta Quadrant and merged with the Kazons. The two species are now the Klazons.
Despite the fact Disco had the Klingons in S1 as the 'enemy'... it would have been nice to at least gotten a 'mention' as to what happened to them by the 32nd century. It would take all of 11 to 20 seconds really.
They're probably keeping their options open and keeping people curious. If they tell us what's happened to the Klingons now then that limits future stories slightly and no one will be wondering about it anymore.
Plus there is no need to revisit the Klingons. Leaving them alone is just fine by me. In fact, it would allow them to try and be more creative rather than going back to the familiar.
Episode 8 Spoiler A DSC Klingon style Mek'leth can be seen briefly in Haz's collection https://twitter.com/gaghyogi49/status/1492573720191373317
I've got to say, never in a million years did I think that in the 32nd Century Spoiler we'd see Changelings before we saw Klingons. Congratulations to the DSC Writers for surprising me like that.
While I get and agree that Klingons have been overused, their absence and lack of a name drop in the 32nd after nearly two seasons is jarring and conspicuous.
Their Augment experience introduced a mutation which rendered them all sterile after twenty generations. Pure blooded Klingons only exist in song and literature now. My head canon. Subject to change, of course.