Based on what Open Source reports are coming out, I think Ukraine has two objectives for this campaign. Pushing Russia back out of Bakhmut, and recapturing Mariople. Which makes sense, as achieving both would essentially reverse two of Russias biggest wins in the war and be an absolute body blow to homefront morale.
Bahkmut isn't just a PR move but would keep Russia's attentions focused for the next 9 months.
Mariupol is different situation; I haven't tried to sort through the intelligence but I had heard Melitopol was a more likely candidate. Minus a Kharkiv like rollup, Mariupol is probably a bridge (or three) too far for this year. Hell, Melitopol might be too ambitious. but the key thing is that those are obvious targets because if Ukraine can take them, or even get close, they will have effectively cut off Crimea. The only supply line to Crimea would be naval or a single bridge. Someone has already struck the bridge, so that likely wouldn't last. And the BSF has been proven vulnerable to cruise missiles, UAVs & USVs, and sabotage. They have the tonnage capability to keep Crimea supplied (Crimea might not have the capacity to offload that tonnage quickly enough) but they may not be able to provide the security required to make that happen.
Russia could try airlift, but that has not been the Soviet's strong suite, plus big transport aircraft would make inviting targets.
Anyway, if a M*pol push is in the cards, it'd make Bahkmut more strategically important. That is, taking either of those cities cuts off Crimea; Ukraine at that point wouldn't need to invade Crimea, they could simply let it wither. Which means the Russian response will have to be a do-or-die attack to dislodge Ukraine and push them far enough back to get Rail connectivity to Crimea restored. If Ukraine can also take a strategic point they could conceivably make a push from deep into Russian lines, that will be mean Russia could not full commit on its counter attack - they moved everything south to save Crimea, Ukraine might be able to push the lines to the north.
That area doesn't need to be Bahkmut, but it fits the bill and has brand-name traction.
Are there viable options to cut off Bakhmut instead of attacking it directly?
Sort of, but both would be more costly than taking Bakhmut. You could encircle, but your pincers would be exposed and require taking lots of territory currently held by Russia. You could take artillery areas and turn Bahkmut into an attrition hell to hold.
I watched a few videos and it seems like Russia may have blown the damn. But not for any James Bond villain reasons involving the NPP plant. They did it because of the Ukrainian offensive. It was a strategic move. Probably not the best. But it seems like it was made under stress and kind of a panic. Probably not the most well thought out plan ever. Also the IAEA says they aren't too concerned over the NPP. There is a second source of water it can use for coolant.
Like I said before, they blew the dam to prevent any possibility of Ukraine doing a Dneiper crossing. The flooding and return to marsh of a lot of the terrain means Russia does not need to worry about having to race troops to reinforce the low-quality 'guard' troops there in the immediate future. They are trading any hope of pushing back into Kherson for a shorter front.
Its clear Russia had the damn rigged to blow if needed, its almost assured these charges are what took out the dam, the only question is if someone set them off intentionally and if so, did they do so because of orders or panic.
The downside to Russia for blowing the dam, as I've seen wonkinated, is that part of the reason Ukraine had not seriously planned a Dnieper crossing was the possibility of just this scenario: Russia blows the damn to flood out a break through. If Ukraine did cross, any troops would need to leave the flood zone in a big hurry, and any troops not pulled back would be cut off on boggy ground.
(also Russia would have a decent case for "military necessity" for exploding the dam in any reparations trials if it was done in response to a push.)
Now that Russia has blown the dam, if Ukraine can identify a good bridgehead, they don't need to be concerned about Russia trying to flood out an advance.