There are some plans to outsource to Ukraine. However what exactly this entails is unclear. The contracts for small combatants are quite juicy, and have a lot of potential for any shipyard that gets them. I.e. the shipyard that wins the internal tender for the first few ships will likely get any future contracts for those ships by default (including export ones). So I would imagine there is a lot of pressure not to outsource those. They're also contracts that most Russian shipyards are capable of completing.
Refiting a giant old cruiser is a whole other story. The project has high risk, requires a lot of funding, and is likely to face major slippages in cost and delivery time. Hence why Sevmash in Russia is the only one to take care of those, and even then more so because it's been practically assigned the role of Russia's large ship builder. Hence why there is a lot less desire amongst Russian shipbuilders to pick up said project. At the same time, in the best traditions of Russian politics and bureaucratics, there is a desire to reward Ukraine, there is money to be spent, so something for it to be spent on is invented. In the end it's not that bad of a solution, granted that the money could've been spent on something far less useful, or just been turned into gas subsidies.
And of course there is the issue that the VMF will get very few blue-water vessels in the next decade. By optimistic estimates I would expect 2-3 Kirovs to be refitted, along with the Kuznetsov, and a few of the project 22350 frigates. A new Slava would at least help maintain some nominal projection capability. Additionally if a single Slava refit can go through, then there is a template and a working relationship to do the same for the rest of them. And in the long run possibly a whole new class of ships to replace them.
