Progozyn and Kaydarov are nobodies. They have about 10 000 each. Rosgvardia is about 340 000 and FSB is about another 300 000. GRU containing Spetsnaz and Alpha Group (kind of special forces and SAS respectively) is of indeterminate size.
These groups have vastly more muscle, the keys to best troops in the state and most importantly information, either through being basically spies or the special investigation teams in Rosgvardia. The theory is that ex KGB run Russia as a collective, (Bortnikov, Nyrishkin, Ivanov, Partushev etc) with a cadre of "technocrats" in the inner circle, Shoigu, Gerasimov, Medvdev, Lavrov) used to do the work that requires detailed knowledge. The Yetlsen oligarchs were kept on to get rich by running the businesses of the country as long as they did not think of themselves as being involved in politics.
Its plausible Russia will Balkanise. but at best Kaydarov can be king of his mountain kingdom, never any higher. More likely the real mass of power in the country, the intelligence service, will remain loyal to the core group who if Putin falls, will find a new first among equals.
My piss poor understanding is that the "capitalists" are on a short leash to a long drop from a window.
The army is under the control of loyalists and allegedly really dumbed down its training so lacks the kind of well educated upper officer corps of other armies.
The mafia is party part of the government and partly controlled through the police and courts.
The people are the real enemy and the real threat, they are kept depoliticised by misinformation and control of most avenues of dissent (a state created by secret policemen).
The battle to replace Putin will be within the inner core unless something catastrophic happens.
With the exception of Chechnya there is no regional opposition and the main power of the GRU, FSB, Rosgvardia and army would mean if the centre came for you it would be over brutally. Plus everywhere is dependent on stipends from the oil and gas.
This is not the only view of Russia, or perhaps the most widely held. But its the one I think works best.