The East vs. West is far more complicated than just Russia and US and only oil/gas. And even though there are only 4-5 actual geopolitical players, this affects the entire world and the rest are picking sides making a big bloc versus bloc.
Of course as you may already know, different countries are acting differently and have different goals. For example India is playing both sides trying to become an economic power in the near future and has the potential. At the same time Turkey is also playing both sides but only to survive.
Even though there are only 4 impactful geopolitical players (US, Russia, Iran, China), we definitely can not limit what is going on to two of them or even a handful like OP did.
To her. Therefore, indeed, many of them will now take advantage of the weakening of the central government of Russia by the war with Ukraine and will try to gain their independence. Previously, such attempts were brutally suppressed by constant repression, but now the situation is gradually changing. The Kremlin's power is now weakening due to the significant absorption of material and human resources by the war, or rather, the weakening of the repressive apparatus. Russia practically does not have its own oil and gas. She shamelessly takes them away from the indigenous peoples of Siberia and the Far East. Defeat in the war will certainly exacerbate these internal contradictions and lead to the actual disintegration of the Russian Federation into separate republics. Great Russia will come to an end.