First, agreed, Putin will never have an ‘official’ successor. He would be far too much of a risk, and Putin doesn’t seem to trust anyone, much less anyone with that degree of influence.
As for what happens, I see three main options - another ‘internal security’ member (who knows where the bodies are buried), a plutocrat (who will promise prosperity for all and mostly for themselves) or a military man (more on this later).
The first will be more of the same, although, as with Trump, it isn’t clear if they’ll have the same overwhelming popular support, without which, there will certainly be power sharing to a larger degree. They’ll probably wind down the war with Ukraine because they’ll be busy pushing blame for it to others, and consolidating their own influence.
The second, depending on the lingering economic factors from the ongoing war, will be very, VERY happy to secure a quick break in hostilities in exchange for an immediate ending of sanctions, and will ride a tide of petro-prosperity into a largely popular rule, but will again, be compromised in their power, sharing with internal security and the military.
The military is the big unknown - if there is ever a general that distinguishes himself in the Ukraine, while not being purged by Putin, they could easily become the next leader, at which point they’ll be more likely to complete their assumption of power by making it a priority to grind Ukraine into dust. They’d also be likely to want to break the power of the plutocrats, as a dangerous and unpatriotic faction in their government, which would let them toss some of the wealth to popular interests while keeping the rest to buy support from their own followers.
So, very interesting times ahead.