Basing 1-2 in the Black &/ Med. Seas would help that, as it's still too far away to the S. Atlantic/S.
Tartus is nothing like the size needed to operate an entire carrier group from... it was a small workshop base that has been slightly upgraded to take more ships, but it is nothing like the size needed to dock six or more large ships needed for a carrier group.
More importantly such a set up would be horribly vulnerable to attack by terrorists... such an attack would have little value for the anti assad syrians but the countries funding them like the US and Israel and Saudi Arabia would love to see such things damaged.
Based in the Northern Fleet fairly quick and easy access via the GIUK gap can be achieved... who cares if NATO can track them through there it would really have little to do with them anyway and if they tried to actually stop them that would be justification for return fire which would pretty much cripple most of the EU so it probably wont happen.
Pacific & the Indian Ocean from Kola & Kamchatka; getting there will take 2-3 weeks.
Exercises will be planned years in advance, and even an emergency will take a few weeks to gather up resources anyway... depending on the situation a few ships can be sent ahead to stabilise the situation or provide a presence for the Russian government to have a say with follow up forces arriving later if muscle is required...
Russia will never be in the position the US is in where it has carrier groups for each ocean ready to operate at short notice... it will be more like France or the UK who only have a few options and much longer preparation time.
Obviously Intel services means it can anticipate situations and send a carrier to a hot spot with further destroyers and support ships to solidify its presence a bit later.
As I have mentioned if it carries 90 aircraft max then it might travel around with half that, but when it arrives on station support ships wont be able to deliver AWACS and Su-57K fighters, but aviation fuel and ordinance for 90 aircraft which is the capacity of the ship, plus some extra stores that could be placed where the full compliment of the other 45 aircraft that are not on board means better persistence and performance because it will effectively have twice the fuel and weapon load for the aircraft it carries than it would normally have if it had a full load of aircraft.
In the empty space where those 45 aircraft could have been they could carry a dozen Iskander TELs with 24 missiles plus perhaps 48 reloads, and with the INF treaty gone they could be 3,000km range models for use against targets ashore... soften up the air defence network of the country that is being visited for instance.
Or they might take UAVs in place of those extra aircraft that they can send into enemy air space and monitor enemy air defences and reaction times and procedures...
In contrast, it took the CV-63 home ported in Yokosuka, Japan just a week to sail from Guam to the Arabian/Persian Gulf in 1998.
For the ground war in desert storm it took 6 months to form up a force... the point is that you can dictate the time table yourself with a carrier force... it can be a fire brigade or a siege engine...
but not enough endurance. Can it patrol for 6 hrs over water 300km away from a CVN?
A lightweight model that is all fuel and radar antennas could easily manage that sort of performance, but as I keep saying a fixed wing AWACS platform would do it better and cheaper and easier for longer...
Inflight refuelling for a fixed wing aircraft is easier than for a helo... and yes I know the Americans have refuelling options for their large helos, but the Russians don't... refuelling a long endurance fixed wing aircraft is more efficient and easier and cheaper.
The joint RF-PRC project will produce such a cargo helo with 15T payload, but it won't be as good for COD due to it's size & conventional layout.
You would want a ground up custom designed aircraft for such a specialised role as AWACS and COD for a carrier... the project you mention probably wont even bother with folding main rotors because it would be an extra complication and expense that would not be used that much in a land based aircraft.
And if you are going to be making a custom designed aircraft then adding wing lift and more efficient propulsion and you end up with a Yak-44 type aircraft.
By the time they have a CVN, those tandem & side by side rotor helos/tilt-rotors will be past their theoretical and unproven stages, as they r needed in many other, non-naval specific applications.
They might, but why spend money on them just in case? There is no fountain of money printing machine in Russia... you actually have to show some real benefits that justify the costs and the risks. VSTOLS are nice toys, but in practical terms if a more conventional model can do the job cheaper and easier and simpler then it is a no brainer choice.
Then why put heavier engines with contra-rotating props on them?! That's what gives the AN-70 short field performance!
During takeoff the whole point of the exercise is to accelerate the air flow over the wings to hold the weight of the aircraft.
A MiG-29KR has a relatively big wing with lots of high lift devices and also rather powerful engines to rapidly accelerate the aircraft over a short distance... it can use the ramp to loft it up into the air when it looses the support of the carrier deck to improve its ability to get airborne.
For a bigger heavier much less powerful aircraft like the Yak-44 having a ramp makes its takeoff performance worse because it is much heavier but has much less power so climbing up a ramp slows it down at a time when it needs to be rapidly accelerating to get to a speed above its stall speed.
For the MiG the ramp is like a jump at the end of its run, and it improves its ability to get airborne and to start climbing, for a Yak-44 a ramp is like tripping and slowing down just before it falls into the water.
The Yak-44 could be fitted with the jet engines of the An-124 and have enormous thrust for takeoff but the size and weight and fuel consumption and drag means it will need to land or be refuelled within a few minutes of takeoff because its normal fuel load will be replaced by a fuel guzzling engine.
Contra rotating propellers like the Bear or An-70 require a lot more power to turn so you need much bigger much more powerful engines to use those.
In fact with the Bear a normal four blade propeller would need to be huge to absorb the enormous power of the engines so having 8 blades in a contra propeller arrangement is a good way to prevent the blade tips from moving supersonically and losing propulsive thrust in use.
Very simply bigger more powerful engines will reduce the range and endurance of the aircraft which is a bad thing.
There is no perfect solution... rocket boosters are dangerous to things on the deck during takeoff and solid rocket fuel is expensive and you would be limited in your AWACS and heavy aircraft operations by how many rockets you could carry.
EMALS, if you can get it working, offers the best all round solution... you can say that the US has struggled with it, but then they have also struggled with hypersonic weapons... I am sure funding for both will be boosted to help sort out problems, though such a solution is not always what is needed...