Until Danilo Skoropadsky (Pavlo’s son) was offed by Soviet agents, there was a significant faction of Ukrainian nationalists who wanted him as Hetman (unfortunately his son Borys hasn’t managed to inspire the same level of sentiment, but speaking as a Ukrainian-Canadian, I think he’d be a great Hetman.)
The Khivan and Bukharan houses are for sure possible, but the issue is both are based in what is now Uzbekistan, so which one is going to rule? There’s the option of a diarchy or Uzbekistan voluntarily splitting itself top properly revive each state, but I dunno. A lot of people associate Khiva with Turkmenistan, since they at least had nominal overlordship over the Turkmen tribes, but keep in mind their capital is in Uzbekistan.
I have heard of some guy who claims the throne of Belarus, claiming descent from the Princes of Vitebsk or Turov or one of the other minor Rus principalities, I think, but I think the jury’s out on his actual legitimacy or if he’s just some rando guy. That said though, a personal union with an Urach monarchy in Lithuania is possible given the strong historic ties between Belarus and Lithuania.
Georgia’s an obvious one given the OTL level of monarchism there is one of the best in the world, however, there’s two branches of the Bagrationi with equally good claims, which complicates matters. I don’t know if one or the other has the upper hand in support.
For Latvia, are there any descendants of the Dukes of Courland and Semigallia still around? I’ve never looked into it myself but that was the closest thing we’ve ever historically had to an independent Latvian monarchy.
Moldova can just reunite with a Romanian Kingdom, so that’s an easy one.
Azerbaijan, as mentioned, has a number of noble families from the old Khanates, but there’s several, so how that’ll work is kinda confusing. Maybe a Malaysia-style rotating monarchy or a UAE-style thing with one over-king.
As for Estonia and the remaining Central Asian republics, I have nothing, if Finland restores its monarchy Estonia might be down for a personal union. If all else fails, they can always import a foreign prince.
There is little practically difference between a constitutional monarchy and republic. I don't see how you are going to get it to be a active political matter in any European Nation or greater numbers than otl without a extremally strong far-right Russian monarchist party.
It’s already happening, monarchist sentiment is on the rise in a lot of republics, and a restoration on popular support is already plausible in places like Serbia, Georgia, and Nepal, and Montenegro and Burundi have already taken steps towards restoration with giving the Petrovic-Njegos family an official role and their new constitution promising a referendum on restoration, respectively (keep in mind, almost no monarchy was abolished with popular support, people seem to inherently have an affection for kings and queens, it may not be 100% rational, but humans seem to psychologically need things like that. To paraphrase something CS Lewis said, if you can’t honor a king then you replace it with some dingus, and the dingus is certainly not the preferable option.). And it’s certainly not inherently a far-right thing either, pretty much all monarchists despise fascism just as much as they do communism, and most from what I’ve seen are very moderate and a sizable number, (especially semi-constitutionalists and absolutists,) are outright apolitical outside of liking monarchy as a system. It might take fifty years or it might take five hundred, but I’m confident that the current time in the sun republicanism has is going to end eventually, there’s a reason monarchy worked across every corner of the world for thousands of years and republicanism was only able to overtake it by a wave of dictatorships, juntas, and colonialism imposed by a small number of naive idealists in what Hobbes called “the aristocracy of orators”. Republicanism had brief flourishing before in the ancient Mediterranean and medieval Italy, but just as it died before, it’ll die again, and with how massively apparent it’s flaws are due to the scale and scope of its spread in the current era, the next death of republicanism might be the one to permanently do it in and push it to the fringest of fringes.