- minimizing public participation in politics
- minimizing interest in anything political
- promoting self-improvement
- promoting the wellbeing of friends and family
- promoting local community involvement
- opaque even to its own citizens and faceless
- theoretically be “self-righting” in response to crises
- positions not popularly elected, any more than electing one’s manager
My brother in Christ, you just described almost every single pro-capitalist dictatorship that has survived beyond their ideologically driven 20-30 years honeymoon period. It's so bizarre seeing these perceived as points of a genuine ideology when veering away from ideological mobilization and trying to have the populace redirect their focus onto self-improvement and family values has long been a reliable tactic used by those already in power to disincentivize popular participation in politics, and thus have continuously shown up in all right-leaning (and sometimes even left-leaning) dictatorships all the way from Latin America and Africa to Southeast Asia and Interwar Europe.
An opaque government that theoretically self-corrects without need of public input is also such a bizarre thing to actually expect from a government instead of something to just take for granted. Even the most rigid of dictatorships have the capacity to self-correct accordingly, with these self-correcting processes usually amounting to the shuffling of ministries, creation or abolition of agencies and the changing of power balances. But nonetheless, all dictatorships have the power to do so because autocracies are structure-wise more elastic than democracies and can function for decades with hacked-together and jury-rigged state structures assembled ad hoc without being slowed down by public mandates or rule of law.
There is a myriad of dictatorships that were ultimately unable to respond to crises and collapsed in response, but there is a plethora more that survived them. But even at the end of it all, no dictatorship has lasted a hundred years, even when those dictatorships were running on a very lean ideological platform like the one that you're suggesting. I would argue that Putin's Russia before the war, and the post-Deng pre-Xi era China both fulfills your criteria. I would argue that even modern Vietnam and Laos, coupled with other places like Singapore and Rwanda also, if not embody, but aspire to the notions you've suggested.
For dictatorships that have endured for a long time, ideological mobilization is a hose turned on and off at will. It is turned on during times when political consolidation is needed, and rapidly neglected when things find stability. Ideology is not something that necessarily prevents self-correcting, but turning on and off the hose of ideology is a toolkit of a dictatorship undergoing self-correcting. That's why we can observe places like Francoist Spain at will switching between the ideocratic totalitarianism and the apolitical market managerialism you're looking for, even without changing too much of the old guard. The same can be seen for Communist China, Putinist Russia, Pinochetist Chile, Libyan Jamahiriya and loads of other regimes.
I don't want to be mean, but what you're looking for basically amounts to "I am looking for a dictatorship that works". Okay? Then find one that works lmao. Ultimately, the functionality of the self-correcting system you're looking for is not dependent on ideology, but the personnel steering the state, and the personnel that determines who steers the state.