It'll remain to be seen whether a New Détente is even clinched at all, to say nothing of its modalities in that event (including speculatively secret clauses), but the scenario is credible enough to discuss considering China’s public signals of interest in seriously exploring its parameters. A lot can still happen to derail that trajectory, and it’s even possible that it wouldn’t perpetuate the bi-multipolar system in which they both have a stake contrary to their expectations, but it’s still worth thinking deeply about.
I think you have been overstating China's objectives in rivalling the US. It is merely doing what a truly great economic power would do. There is no similarity between the US and West's history of predatory rape and plunder, colonial and imperial, and that of the peaceful history of China.
China was the world's biggest economy naturally for 18 centuries until British, European and American colonial adventures and opium war crimes devastated it. Nothing suggests that China intends to loot the countries it has spent $4 trillion building infrastructure across Eurasia for.
The US has trillions to spend on warcrimes but won't even rebuild it's own crumbling infrastructure!
And the theoretical nonsense you repeat about bi-multipolar and multiplexity is simply a move by countries that were bullied, looted, colonized etc for centuries, and continue to face such threats from the 1000 military bases of the US - to seek a different, better and or trustworthy partner in China.
India did not support Russia principally to prevent Russia's overdependence on China. India remembers the Soviet intervention in the Bay of Bengal in 1971 which sent the US and UK navies packing.
Hence PM Modi recently described the Russia-India friendship as 'unbreakable'. In the face of massive US pressure on it to condemn Russia and not buy Russian oil, this is a colossal F.ck You to America. Along with India now making Russia it's # 1 oil supplier.
There are a lot more things at play here than your assumed US-China interest in bipolarity.
Without China also refusing to condemn Russia and (by some reports) rerouting Russian oil to Europe, could Russia survive the monster hybrid war the US is leveling against it with full British and NATO support?
The move to multipolarity simply CANNOT happen without China, and China's continued growth and leadership in the New Silk Road aka BRI.
China is going to be the biggest alternative pole to the US, and will be the dominant global economy once the US is displaced as hegemon.
I don't think either Russia or India doubt that. But the massive oil and gas and other rare resources of Russia are also crucial to both China and India and the rest of the Global South.
So all these countries plus other powers like Iran and Turkiye (which just rejected US hypocrital condolences for the terror bombing in its capital, making it more likely to tilt towards Russia et al) will have to ally with each other to break the Western dominated world order, or replace it with a major alternative.
Indian billionaire Adani just opined that India would be the world's second biggest economy by 2050. He knows which the largest one would be - China.
All this assumes the world can survive the increasingly dangerous escalation of US - China tension in the Taiwan Strait. And the proxy war v Russia, attempts to destroy Iran etc. All are potentially catastrophic possibilities given the warmongering history of the US and its vassals.
For now India appears to be avoiding serious consequences for its defiance of US pressure, though the US's coup in Pakistan and statements about 'Azad Kashmir' have been designed to retaliate against it.
I think a simple explanation for the 'olive branches' is that China knows the US is seeking to provoke it to invade Taiwan, and will keep escalating those tensions.
For the unquestionably declining hegemon, that is it's response to it's dramatic loss of economic and diplomatic power.
China is simply seeking to prevent a war from breaking out.
I think you are mistaken about Chinese politics. Putin held his first speech with a clear warning to the West in 2007. But it took him 15 years to find out that the West was not serious at all in their attitude to Russia. China is still exploring the attitude of the West towards China. I find no other explanation possible for the time being. But it is of course important that India again take its position as a balancing power. In Europe there is no such power any more. And the other big powers still has some road to travel.