With nearly a dozen carrier battle groups, you can control seas, project power, etc. With one or two, it's not as much that you can control. For Russians in particular, with their main idea of carrier aircraft as anti-air defense (PVO) beyond the range of their navalized S-300s and S-400s, the safest bet would be to develop STOVL aircraft for use off of their helicopter carriers that are supposedly under construction.
This would be terrible. Smaller STOVL carriers have more restrictions in terms of what weather they can operate in. The aircraft they fly also tend to be less capable (unless you count the F-35), and Russia would have to develop a STOVL 5th gen from scratch. If Russia goes the carrier route, in my opinion they should go for a large nuclear powered carrier with eventual navalized Su-57s. Half-measures are not the way to go, and Russia can't afford their own F-35 equivalent. The best we would likely see in a near-future Russian STOVL would be a reborn Yak-141 with new avionics and an upgraded engine, and that's just too little too late.
On a side note, with 3 aircraft carriers, the Northern Fleet could maintain one near home, one on deployment, and one on maintenance quite well. This would let them effectively support the Mediterranean squadron, or even conduct longer voyages into the Indian and Pacific oceans for joint training with India and China. It wouldn't give control of the seas, but it would provide a serious headache for someone planning against the VMF. It would also allow a Syria-style operation without need a local airbase.
IMO LHD are more than sufficient for Russian needs. Their main ship and land attack vessels remain nuclear SSGN and Yasen has no parallel in the world. Carriers are limited in the way they cannot take off strategic bombers, large AWACs, large aerial tankers, large ASW planes, are limited to fighter jets. LHD are far better at supporting amphibious landings.
Yes, no parallel in the world, but with torpedoes that belong in a museum. And just what is the situation with the anti-torpedo system for the 885Ms? I suspect that for all their advantages the Yasen class will be in serious trouble when going up against either US/Wester ASW aircraft that have gotten very
very good, or against western subs due to ridiculously inferior torpedoes. None of this is to say that Russia should stop building the type, or that they're useless. They're very useful, it's just not a good idea for the VMF to put all their eggs in the Yasen basket. Russia should reduce the side of the SSGN fleet to 12-16 vessels instead of the current 22, and focus on better maintenance turnaround times. The spare funds should be funneled towards potential large surface combatants.