His party really only has himself as the head, the Communist Party is the second most popular (even if it’s less radical than the name would have you believe). A joint Communist-beamed Putin and Communist Party alliance would definitely be pushed back against by the domestic bourgeoisie, but the basis for Soviet nostalgia is strong enough in the public.

it’s OK I’ll set the ray to Xi Jinping Thought

I feel like Putin is smarter than that. After however many decades in the spying and politics games he’d be well aware of the need to defang them before revealing his new power level.