The EAEU with Russia, Belarus, Kazakhstan, Kyrgyzstan and Armenia as current members aims to offer economic integration to the former USSR space while advancing some sort of integration with the EU. Brussels for its part is more interested in fragmenting the post-Soviet space attracting Ukraine, Georgia and Moldavia.
Ukraine, before Maidan, was supposed to be a bridge between the EAEU and the EU. Now, we have Kazakhstan as the pivot between the EAEU and BRI. Add to it that Kazakhstan is also a key member of the Shanghai Cooperation Organization and a founding member of the Asia Infrastructure Investment Bank.
We should always remember that President Xi Jinping officially unveiled BRI in Astana, in 2013. The key railway link between the Chinese plains and Central Asia via the Eurasia Land Bridge goes through Alashankou in Xinjiang; the de facto Western Gate of BRI, China's largest dry port, and a companion to another hub, Khorgos, with its twin special economic zones serving both Russia and Kazakhstan.
China is linked to Kazakhstan by a "comprehensive strategic partnership" similar to Russia's, in effect since 2005. Nazarbayev is betting simultaneously on China and Russia. With or without a presidential title, the name of the game will continue to be Eurasia integration.
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