A side from the shipyard there are hundreds of companies that supplies the building effort of an aircraft carrier. Those companies are spread throughout the former Soviet republics and many of them have long since then close their doors. For Russia to build that carrier its not enough to have a good design bureau and shipyard but they have to recreate that entire industrial base. That is at this point unlikely to happen. The Russians can build that ship only if they can get significant foreign assistance. That assistance won't be coming from the West these days.
Well, given the economic conditions necessary, and the time, the Russians could do it. They did it before.
But as you say, almost all of the industrial base necessary has long since gone out of business, so they would have to start over.
But, they have the technical design capability, and the basic underlying resources. They just need the time, the money, and underlying infrastructure...and that will take a long time, if they do it at all.
