A lot, with a lot more yet to come? Ok, so it seems(?) that the dam has escaped being entirely self-scoured away, which has prevented a full on escape of water (or as nearly full on as a hundred or so km of backwater, at its widest above 10km in width, and of an average depth I've not looked into, can possibly have escaped... it's not Fortress-water with teleporting to the front, even). Instead it's as if the most insane dam-manager has opened two to four times as many outflow gates as he actually had available to him. Which is bad enough, creating a new lake downstream that's more than even the traditional flood plain might become after the worst (pre-dam) upstream rainfall accumulation.
So far, it has reached its peak, from what I've seen, so the floodwaters probably won't rise more (perhaps a bit more at the outlet into the sea, due to natural lag), but the tap being turned on like it has is going to be a constant pressure on architecture and natural landscape currently inundated with more than a few centimetres of flowing water (water is dense, and has momentum - and more water constraining it from flowing sideways - so stationary things like buildings and trees are going to be under pressure by any flow striving to go through where they happen to be) going to be under strains they were never built/grown to handle... Plus be now sodden.
If the current "constant rapids" going through the gap starts to significantly shift even more of the dam structure (and/or move and set off any as yet unexploded mines previously laid around it, creating other opportunistic points for water to swirl in depressions and start to gouge more of the structure away) then the tap gets turned on progressively more than even now, which might mean different things to those below (where the inundated river is now a wide flood-plain lake, it'll take a lot to raise the level by even a little/creep a little way more up onto the current dry highground; any geographic pinches will suffer more, though, as the additional accumulation of flow finds its options more limited and it bunches up again). If it gets gradually scoured to the very dam-edges (one imagines the construction wasn't made into valley sides significantly weaker than the man-made structure, but it has been known!) it'll likely get no worse downstream, time-delayed by distance, than with that peak outflow, but it'll be bad enough.
And then the wait (in normal times, though most people will still have... well... war-problems to deal with) as the upper lake empties sigbificantly and the flow becomes much closer to 'normal' river at spate (but some draining away of the inundation will start, as it hits a dynamic equilibreum with the current conditions).
In peacetime, it'd be nigh on impossible to repair the dam any time soon. Helidropped mega-sandbags can work on smaller structural defects (e.g.
this and
this near manor incidents), to stabilise matters, but the raw logistics in the case of this breach are way beyond that. Perhaps deliberately grounding/scuttling barges across the gap might be tried, but too many variables (too wide a gap for a single vessel, the water dynamics might mean extra scouring round the edges/underneath any vessel, risk of impacting the dam wall and dislodging more of its weakened structure, risk of the vessel(s) just twisting through the gap and becoming an additional downstream hazard ...at least until it hits something else fairly solid), and I have no idea what the depth is (originally or, more importantly, now) immediately upstream of the breach. And... you know... with the very opposite of cooperation being possible, I don't even imagine there'll be many expert assessments made (overflying camera-drones are being shot at, obviously!).
Really, the sum total of the damage is massive but will have to be totted up much later. That's just the 'conventional' flooding issue, minus issues of loss of water to ZNP/Crimea and whatever regional agriculture was still occuring beyond the actual face-off zone. It probably distupts plans for both sides' militaries (for both attack and defence contingencies), either locally or forcing extra attention elsewhere because it 'simplifies' the issues in the affected areas by sheer exclusion, and even if the breach was a deliberate military act (the most charitable interpretation I've seen is that mere 'bridge denial' demolition went seriously wrong, or mines that had been laid on the bankings shifted and went off in waterlogged ground to trigger yet more damage), I doubt the plan was for things to turn out like this. Dam breaches are a blunt instrument, not exactly a Nazgul-foiling masterstroke of planning.