Dam you know something is a bad idea when I and Garry agree.
I am not always right, and SS is not always wrong of course, but they went down this road with the Yak-38, and the west went down this road with the Harrier and Sea Harrier... the small carriers these aircraft operated from were not good... the new British carriers are similar size to the Kuznetsov and the next French carriers are similar is size and plan to the Ulyanovsk at 75K ton with nuclear power and cats... it is not an accident that US carriers kept getting bigger, but US carriers are intended as strike platforms... a US carrier group is a US strike carrier at its core with US Navy ships around it to protect it... the US carriers don't protect US ships, the US carriers provide the aircraft, just like the US AF does the war and the US army takes and holds the ground... if the US could fight from the air only they would, whether that is USAF or USN air power... it is more hands off, and it makes their technology advantage against most third world countries a bigger advantage than it would be against an enemy with an IADS like Russia.
The Yak-41 was never complete and it was cancelled because it had lots of problems including the fact that it was never going to be a better carrier fighter than a MiG-29 could be upgraded to being... but was more vulnerable to crashes and battle damage.
Scuttlebutt is that it will be a 5G light fighter to complement the heavy Su-57.
The fact that they are talking about it at MAKS suggests they want foreign investors to help pay for it much like the US used its allies to help pay for F-35.
If Russia did develop a modern VSTOL, who is to say it would be for naval aviation?
For land based fighters VSTOL is irrelevant... even in Russia with a fraction of sealed roads per head of population compared with most western countries there is more flat paved motorway than HATO has cratering munitions so they will always be able to find the 300m of flat paved runway they need to operate fighters.
For bombers and big aircraft not so easy, but those airfields are generally rather well defended.
It would probably be more useful as a front-line CAS fighter, able to support army units from unprepared fields behind the advance, and do so with a rapid response time.
There are no VSTOL fighters that can operated from unprepared fields, that is just bullshit... since when has the Harrier ever operated on dirt runways... or something like this:

The Yak-38M were tested in Afghanistan in the 1980s and were awful.... like any VSTOL fighter when their jet engines rotated 90 degrees down to provide lift it shredded the ground and sent great columns of dirt and mud and crap into the air... much of which entering the air intakes and destroying the engines.
If you can't find heat resistent hard surfaces you have to have it with you like PSP (pierced steel planking).... it would be cheaper and easier using attack helicopters most of the time.
I've often wondered if Soviets/Russians ever developed CAS aircraft that use diesel instead of (kerosene-based) jet fuel (that would hugely simplify logistics if aircraft could refuel from Army fuellers).

Exhibit A.
Russia itself needs a single engine VTOL for its future heli carriers and why not for it airforce.
Russia already developed a VTOL fighter for its helicopter carriers... it is called Ka-52K and has full AESA nose mounted radar for the job.
Russia doesn't need VTOLs.
Russia has already been down that road and it was a dead end.
Unless they have some secret new plan to provide VTOL performance without all the serious and performance limiting problems, then there is really no value in a fixed wing VTOL fighter.
I doubt UAC would choose to develop an aircraft solely for export with no domestic orders whatsoever, but if they did I would be impressed with their confidence and more so if it picks up orders.
There is a large market for a MiG-21 replacement that is affordable.... the current MiG products of the MiG-29M and MiG-29KR and MiG-35 show they have a cheaper simpler model with growth potential to the expensive model and they have a naval carrier model.
They have said a single engine which suggests no lift jets, which suggests to me that VSTOL is unlikely as well as being undesired... a modern 5th gen fighter with a thrust to weight ratio that is 1.5-2 to one should be a very sprightly performer but lacking differential roll control with just having one engine nozzle would certainly limit potential performance.
And for a potential future large carrier I'd rather they bring the naval Su-57 into play rather than some gimped single engine.
The VSTOL might just be for export, the helicopter carriers should stick to helicopters and a fixed wing carrier supporting the helicopter carriers could have Su-57 and this aircraft in combination to increase numbers... but not as a VSTOL, but as a conventional take off and landing aircraft like the Su-57 would.
Smaller aircraft that hang around the ships is a good thing for an air defence carrier.
Especially if they can be more affordable to buy and to operate.
Most have small heli carriers of something like Kuznetsov that can't carry regular planes so such 5th gen vtol can be of interest for them.
In the Russian Navy these new 40K ton helicopter carriers are actually landing ships and the Russian Navy Infantry don't need a Harrier type aircraft to support landing operations when Ka-52s exist, not to mention their new helicopters on the way... I would say it would be more valuable getting Mi-38 helicopters on their helicopter carriers than VSTOL fighter aircraft.
Their new carrier is likely to be bigger than the K but the K can already operate fixed wing CTOL fighters anyway... it only would use cats to get AWACS like heavier aircraft airborne.
It's definitely for VKS as well as export, nobody develops brand new plane without domestic orders
They might be interested in international partners to share the cost and the risk of development... the announcement at MAKS suggests it will be export oriented...
As for S/VTOL I think that airplane is designed with possibility of adding that option later but basic model will absolutely be standard take off and landing version, VKS wants their stuff straightforward and fast and they are main customers here regardless of what advertising says
It was the V that turned the F-35 into a dog... the internal space to allow a large engine powered fan be placed inside ruined its aerodynamics, and the amount of internal space such a fan occupies ruins the range performance of the aircraft when it is fitted too. Even the Brits bought the cat launched model...
Any later investments in development of any S/VTOL version would indicate that they plan to build way more than just 2 of those helicopter carriers
Any investment in VTOL will be covered by foreign investors, but I am pretty sure they will keep a careful eye and unless serious breakthroughs are possible it will be ditched or separated from the core fighter which will be STOL... like any 5th light fighter should be... big engine, light weight aircraft, all weapons normally internal only so low drag... it should be a very STOL aircraft quite naturally.
Should point out that the LMFS and PAK Sha projects (specifically replacement for MiG-29/35 and replacement for Su-25 programmes) are different and separate as attempts to get the light fighter aircraft to replace the CAS aircraft have all been failures on both sides, whether it was air to ground versions of the lighter fighter (MiG-29 and F-16(A-16)) or light aircraft like the Yak-130 variants... the problems of protection from small arms fire requiring armour and for light fighters to be light and nimble are too contradictory...