A carrier is a 3rd world policing
tool.
The west have used carriers to impliment imperial ambitions... but also to secure their own sea lines of communication and commerce.... otherwise why would UK and France need their own carriers? They have them for situations where they can't get the US to join in... in other words when their interests require action but their other allies are not interested.
Russia has no real allies with aircraft carriers that they can rely on, so they need their own carriers.
The alternative is for Russia to rely on others to protect Russian interests around the world and you and I know that isn't going to happen... in fact the US Navy will actively work against Russian interests just to be bastards... the US is in Syria just to be assholes to Russia... they could care less about the Syrian people and what they want or need.... they are supporting terrorists and murderers and criminals in Syria...
In that function, Russia needs to be able to counteract yanqui aggression against 3rd countries.
Russia does not need carriers to become the new world policeman to save the day and foil the evil plans of the US. Russia needs to be able to help allies and maintain contacts with countries otherwise out of reach from other Russian assets and forces.
Why would Venezuela maintain good relations with Russia if the result is going to be crushing pressure inflicted by the US... Russia does not need to be able to defeat the US Navy, but it needs to be able to send ships to support Venezuela and other countries around the planet to relieve any pressure the US puts on them.
Sending them food or medicine or equipment to process their own oil into fuel they can sell on the market... sending them farm equipment so they can develop their own food production capacity... their climate is different enough from Russia that Russia could sell certain types of food that don't grow well there and buy foods from Venezuela that don't grow well or are expensive to grow in Russia...ie mutually beneficial trade and cooperation.
Russia has a bigger sub fleet than China still I think. Russia has tons of subs and always has. Its overkill.
Russia is making excellent progress and is making new subs that are second to none... they seem to have the corvette and frigate designs that they want so now they need to start producing them in significant numbers and to start looking at destroyers and some cruisers.
The upgrades of the old ships... old destroyers and old cruisers should be an opportunity to test new large radar arrays and new large sonar arrays that simply wont fit on smaller ships... on the upgraded ships they can bug test and refine the designs so that when they are ready to lay down new destroyers and new cruisers the sensors and some subsystems will be mature which will reduce risk and make designs easier and less likely to have serious problems.
They need to have destroyers in production and be laying down a cruiser before they consider laying down a new CVN in my opinion.
New equipment tested in the CV Kuznetsov will be interesting and will help in finalising the new design but they need to get the K back in the water and operating for those tests to be done... a couple of years to test in different ports and different climates/seasons and then they can apply what they have learned to perhaps a redesign/upgrade, or prototypes for production which can be integrated into the new designs.
Take some of that sub money and build a brand spanking new carrier decked out with su 57's FFS. It would be a display of Russia's naval and aviation capabilities.
Would look better with the escort of some brand new destroyers and brand new cruisers. The Kuznetsov will look good with two Kirovs and some upgraded Slavas and Udaloys in escort too.
They won't sign any contract for a carrier before they finish the heli carrier for sure which could take 12 years max.
Assuming no cockups the 2 helicopter carriers currently in production will likely be followed by two more the same, so your 12 year estimate is probably rather accurate.... but the fact is that in 12 years time they will have completed production and have about 40-50 Corvettes spread across 5 fleets, and probably about 36 Frigates spread across five fleets and will be in the middle of producing 24-26 destroyers for spreading across four fleets and likely laid down at least one new cruiser of which they will probably produce 8-12 with 2 or three in each of the four fleets and a lot of the cold war boats will be entering the reserve or scrapyard... so by then a new CVN would be a good idea to lay down... but that will take at the very least 6 years... they should be good at the modular production of big ships by then and by the time it is finished there should be a variety of manned and unmanned aircraft to operate from them.
And Russia needs all new subs it can build, not less. Alot of older Sovet era types need to be replaced.
Production is increasing and the new types are very capable. Most subs however have a very specific role and many are only of actual use during WWIII, whereas aircraft carriers will be more useful in both peace time as well as during limited conflicts.
China can't compete.
Fortunately China does not have to compete. Russia is not their enemy and China is not an enemy of Russia... it is the US that is adopting that role, which will be a real challenge for China... though made simpler because for now China is only interested in a fairly limited region but later will expand, while the US has to cover all the worlds oceans... much harder and very distracting.
Even an USN supercarrier has just 48 fighters max,
That is because they also carry strike aircraft... which also require fighters to support which further reduces the number of fighters available to support operations defending the ships.
A good rule of thumb is that for every 1,000 tons of ship weight should equal one fighter aircraft... so for instance the CharlesDG it carries about 30 Rafales and is 40K ton... a 100K ton carrier should be able to operate about 90 fighters...
Obviously most of the time they wont operate with that many fighters on board, but with stores and accommodation for 90 fighters it means 50 fighters can operate for much longer and have more weapons at their disposal and you can always fly extra fighters to an area and out to the carrier to boost numbers.
When the full compliment is on board the deck is usually full so to take planes down into the hangar deck for maintenance or inspection you often have to shift around the other planes to make space... a massive game of 3D tetris... and pain in the ass...