Issue with ship manufacturing ability could be only secondary.From what I understand the Steregushchiy corvettes (20380) and the Admiral Grigorovich frigates (11356Р/М) were basically meant as a low tech replacement for their older ships until more modern alternatives like the Gremyashchiy corvettes (20385) and the Admiral Gorshkov frigates (22350) became available. So they were never meant to be in production for a long time.
The Russians seem to have taken an excruciatingly long time to debug the more modern AESA radars and digital combat systems on the new ship classes. Add to that the issue with lack of engines from Ukraine and Germany due to sanctions. Both these factors basically put the kibosh on any chances those programs could proceed at a decent pace. The engine issue is especially clear in ship classes like the Buyan corvettes (21630/21631), or the Admiral Grigorovich frigates (11356Р/М) which suffered long delays. The modern combat systems delays are particularly evident in the Gremyashchiy corvettes (20385) and the Admiral Gorshkov frigates (22350).
Still, I agree with you that it is unbelievable how slowly Russia's shipyards can produce some ships. I mean just compare the time needed to produce a Gepard class frigate and a Steregushchiy corvette. Both ships have a similar displacement and more or less similar weapon system level. Yet the Steregushchiys take twice as long to build. It seems to be a popular idea among Russian media to attribute the delays to corruption. But personally I think the delays are because the ship designs are simply not adequate for rapid production. Particularly the Steregushchiy/Gremyashchiy corvettes. Too many blocks and parts. There are also delays because of funding issues. I mean sometimes ship construction stalls 1-2 years waiting for funding to come. This is no way to run a business. The government should do block purchases of ship types. At least they seem to be starting to do this with the nuclear submarine program. Also they probably should have focused their purchases on less shipyards. By only giving a couple of orders to each of several yards to keep them all afloat you never get economies of scale from mass production.
I think right now the issues with the combat systems are basically fixed. But the issues with propulsion still remain. Russia simply does not have enough naval engine production but even worse it seems they can't even adequately produce reduction gear and transmissions.
Anyway, the Russian naval industry looks like a basket case. I think the Admiral Gorshkov design is now adequate and they should produce it at another site to increase production rate. They also need to figure out some way to speed up corvette construction and like you said design and manufacture cruiser ships.
Personally I think the Project 20386 corvettes and Project 22160 patrol ships are a bad idea. The Project 22160 at least is being built reasonably quickly, but the equipment level of these ships is just too atrocious. These ships are LCSskies. The ships are basically a hull with a dinky little gun and little else. They provide really poor combat capabilities.
That could gives month rather years to the schedule .
It is more likely issue with the supply chain, probably many cases they have to make companies from nothing to manufacture parts.
That can increase the lead time and cost by magnitude(s).
And the naval stuff could be fourth priority compared to strategic / land and air forces.