To me the real hunks of junk are the Slava class cruisers.
Just compare a Slava class cruiser at 10k tons displacement with an Admiral Gorshkov class frigate at 4.5k tons displacement.
A Slava cruiser can carry 16 anti-ship missiles, 64 long range SAMs, 40 short range SAMs. The SAMs are in revolver launchers. So the ship cannot properly defend against a saturation attack.
An Admiral Gorshkov frigate can carry 16 anti-ship missiles, 32 long range SAMs. The SAMs are in VLS cells. You can quad pack short range SAMs into the cells.
While the frigate can carry less SAMs they are in VLS cells so it can better defend against saturation attacks.
The Varyag has basically had the same maintenance as the Moskva. The Moskva had known issues with its fire fighting systems and they never bothered fixing them. The only Slava class which was properly upgraded was the Marshal Ustinov. Even then this was basically constrained to the electronics, combat systems, and the fire fighting systems. They did not upgrade the weapons systems.
The Kirov battlecruisers have a large upgrade potential. They also have an advantage in that you do not need to refuel them and you can go on long distance trips with them. Given Russia's lack of overseas naval bases, if for whatever reason their navy needs to go on a long distance deployment, the battlecruisers are basically the best option to do this. The question is, is it worthwhile to upgrade these ships, or are you better off building new ones. Currently the Baltic Shipyard, which built the Kirov battlecruisers, is busy building nuclear icebreakers. These currently have a higher government priority since they are needed to open up the Northern Sea Route for direct trade with Asia. They will be building icebreakers until basically the end of the decade. So I think it is unlikely they will build new battlecruisers before that. So I think it makes sense to also upgrade the Peter the Great. You won't be getting any more ships any time soon, since the shipyards which make these ships are basically all loaded.
Once they upgrade the shipyard at Severnaya Verf, maybe then they can make more frigates. But right now they are also fully loaded. The Amur shipyard needs to finish its current corvette program before it can build any frigates. Maybe you could build more frigates at Yantar in Kaliningrad, or at Zaliv in Kerch. But right now the main limiter on increasing frigate construction seems to be production rate of the naval propulsion units.