There is some reason to disbelieve the official numbers. They started dropping rapidly under Putin, while the number of unidentified bodies processed by the health system climbed more or less identically: https://www.noahpinion.blog/p/russia-is-not-actually-a-very-...
What are the sources of the alternative numbers? (Up to Jamaika, 83%, more than 60 percent, etc).
As for the rates raising in 90-ies and then falling back down, that's understandable, if you know what were the 90-ies there. The same happened in all other post Soviet states.