There are certainly no visible signs of that so far, and given how Prigo "coup" went I think it's pretty safe to say that there no actual instability within. Literally everybody in the government or the military immediately pledged support to the government. If there were any dissent before that, it's most definitely been rooted out after.

The biggest rift in Russia is caused by highly divided support for the war and for further mobilization. Majority of people stopped having positive outlook on the west and are in favour of self-sufficiency over Russia's government seeking substitutions from other countries, which causes some displeasure. General opinion of Putin is about neutral-negative, there is not much respect for him but he is seen as necessary. Overall the government is perceived as incompetent/corrupt (even before the war) due to it not fulfilling promises and shitty budget allocation on anything that is not a big city, and there is a desire for a stronger leader against the west, which could either be good if the communists manage to exploit that after Putin leaves or extremely bad, because a lot of hardliners aim for that role. Currently Putin is in a fairly stable position since dislike of the western countries vastly overshadows dislike for Putin. I don't see the cracks that would lead to him getting deposed yet (Its gonna have to be more than general dissatisfaction) so the best thing is to continue to observe how things play out.