At this point the alone concrete project of aircraft carrier is the Project 23000:
The ship will carry 100 aircraft including the navalized version of the T-50 PAK FA stealth fighter, Mig-29Ks and Yak-44 early warning and control aircraft.
Very likely the bolded in red are the 2 aircrafts Bondarev is talking about. Obviously and logically, the fighter aircraft to replace all the current shipborne fighters will be the Su-57 (T-50). The second plane to replace the entire Russian shipborne fleet would be this new early warning and control aircraft. The MiG-29 is of a previous generation.
While Russia anticipates fulfilling the fighter/attack and utility roles with its current aviation projects, its AEW&C capabilities are very anemic. At the moment, the Russian Navy uses Kamov Ka-31 Helixes to fulfill the AEW&C role- essentially refitted coaxial helicopters that carry a large rotating/folding radar antenna underneath the fuselage. While the Helix does actually perform somewhat as needed while deployed aboard the Kuznetsov, it just doesn’t live up to the mark set by fixed-wing AEW&C aircraft like the E-2C/D Hawkeye, currently in shipboard use with the United States Navy and the French Navy. A limited range and a very limited onboard sensor suite are two of the Helix’s biggest flaws. Therefore, Russia if builds a better carrier than the one they have right now, they’re going to need better AEW&C aircraft too. The article in IHS Jane’s did state that Russia expects to build a jet-powered airborne early warning aircraft. However, an AEW&C jet would, in comparison with a turboprop version, likely necessitate heavier maintenance, fly with a reduced range and, in general, just cost a heck of a lot more. So it might actually make more sense for Russia to consider building the propeller-powered alternative instead, and luckily for them, in designing a brand new AEW&C plane, they can call upon the scrapped Yak-44 project.
In this quote we can see how some media identified this new project with the Yak-44. Like que Yak-141, the Yak-44 was a project cancelled with the fall of the Soviet Union, but like like in the case of the Yak-141 some media identified the project of a new early warning and control aircraft with the Yak-44 project because this was also the role of the old project.
For the following years, a new early warning and control aircraft (in fact a shipborne maritime patrol aircraft) design would be totally different. It can be VTOL and it can be unmanned. The words of Bondarev about a new VTOL plane make sense, but not like the media is taking them.
Finding new real Russian VTOL projects, like in the case of the Project 23000 aircraft carrier, this is the most modern project of Russian VTOL aircraft that we can find (obviously far closer to the V-22 Osprey than to the Yak-141):
This is the form of the newest Russian VTOL projects. A new VTOL early warning and control aircraft can emerge in the future following this line.