That's true, I always thought they'd pursue damages whatever cost simply down to principle. Unless they're thinking about another (cheaper) way to stick it to the French in response.
It's more likely that they don't want another issue to fight over with the west. Especially a relatively friendly country like France.
I think the Russians would be content just for a refund. The French are quite pro-Russian and while litigation might succeed it would be a strategic loss given the damage to that relationship.
This is probably spot on. Given that they already have problems with Europe over Ukraine, I don't think they want to make it worse.
They could just be biding their time until things settle down so they can restart this project or kick off a new one in a few years.
Personally I am surprised the project ever got off the ground after what happened in Georgia, I know it was that conflict that highlighted the need for such vessels to the Russians but the pattern of events that led to it should have been more than adequate warning of what was in line for other neighbours Russia thought may be straying to close to the west. It was glaringly obvious that that Russia wanted the ships to better be able to project power and to give them another option, another way into any troublesome neighbours or republics.
There's nothing surprising about that. Think back to the EU commission report on the War in Georgia. The OSCE essentially confirmed the key points of the Russian claims, namely that Georgia struck first, hit Russian peacekeepers there on an international mandate (one the Saakashvili government itself signed), and violated international agreements in an internationally recognized conflict zone in an attempt to resolve the conflict by force. Honestly if it wasn't for the current conflict in Ukraine, France would be extremely happy to deliver the ships, and help with the construction of another 2 or even more vessels. It would have given French military industrial companies unprecedented inroads in the Russian market, and given problems with Russian shipbuilding, it could have led to greater French involvement in Russian Naval programs in general.
IIRC France is trying to flog SSK's and MdCN to Poland, could potentially be a larger sale than the LHDs (in my mind, i have zero numbers to back that up) to a friendly state than a lower sale to an unfriendly state.
France and Russia are actually rather friendly. I think that France is cancelling the contract because the war in Ukraine is not winding down, and they can't hand over the ships unless the war comes to an end. While there remained hope for a relatively quick resolution, they kept talking about potential future deliveries, but now it looks like the situation in Ukraine is going to be around for a while.