No, I don't buy this at all.
For one, Kovalchuk is on the record saying the most conspiratorial, chauvinistic, and insane things about Ukraine and the "anglo-saxons", probably superseding those of Patrushev himself. He was one of the main influences on Putin for this war to be started in the first place.
People like to speculate about the "towers of Kremlin" which vie for power behind Putin's back. I think there are really just two towers that hold real power - the "siloviki" (led by Patrushev and FSB) and Putin's personal friends and family (Rotenbergs, Kovalchuk, etc.). Just like the two groups Girkin outlined in his post.
The main difference between these groups is that siloviki are independently powerful and Putin's friends absolutely hang on Putin remaining in power. Once he's out, they will have no protection and no military or political resource to keep what they currently control.
It was said that Prigozhin was originally affiliated with Kiriyenko (Kovalchuk's group). But for the reasons mentioned above, I do not believe the latter group would ever try anything that undermines Putin's power. So I am convinced that Prigozhin's coup was either staged by an FSB-affiliated group (him being a double agent) or that Prigozhin actually went rogue and acted against Kovalchuk's interest, probably still aligning with the siloviki as the result. So him still being alive means a win for siloviki and Putin's buddies being weakened.
Girkin is affiliated with FSB likewise. So this post by Girkin has to be an elaborate ruse, a psyops. To convince the rising Russian fascist public core that Prigozhin is still a Kovalchuk's guy and Kovalchuk and Co want to end the war. When in truth, it has to be vice versa. Putin's life and career depend on how this war goes now. So "friends and family" absolutely are in till the last soldier. While siloviki have not much to gain from prolonging the war or escalating it. I think siloviki are the ones working toward ending the war, but they want to blame Putin's friends for this so that they can keep the support of the rising Russian fascist irredentist core.