EL8 CHART, page-18

Indeed, there's already some effect in terms of Kazakh uranium being considered higher risk (so even moreso than after the recent protests, as a trader/utility you'd probably rather not be 100% exposed to Kazatomprom in your future contracts) & also Kazakh uranium coming via Russian centrifuges in the case of Swedish utilities cancelling some supply agreements there (and perhaps that to grow). But in terms of Russia/Kazakh instability, definitely something close to a "black swan" event or at least extreme left tail (well, right tail for neutral/western uranium sources).

The way I'd see it progressing would certainly not be a Russian "invasion" of Kazakhstan, as you say. I can imagine that if Russia wanted more centralized control over Kazakh resources, though, under the auspices of stability & cooperation it might be "invited" to move in troops as a precautionary CSTO-related measure, effectively giving it a bunch of hard power leverage over Kazakhstan without officially affecting relations, making any concrete demands, attracting heavy sanctions, etc. In theory not affecting anything, just ensuring Kazakhstan stays tightly coupled with Russia's fortunes & continues to export yellowcake via Russian enrichment facilities. This doesn't seem like a super crazy outcome to me - while I do not at all see Kazakhstan doing anything drastic like try to exit CSTO or outright ally with the west, I can see it trying to have its cake & eat it in terms of tying its economy to the west (think NZ continuing to trade heavily with China recently despite being a five eyes nation), and can also see it economically trying to jump ship and tie itself more closely to China which would be a quite viable short hop given relations between the 3 are RELATIVELY warm (if a little tense at times), which again I'm sure Russia would like to avoid.

Status quo is still the most likely outcome, but "Russia solidifies its hold via some fairly coercive diplomacy" or "Kazakhstan pivots harder to China" both seem far more likely than "Kazakhstan pivots economically West and Russia allows it"