I mean among the four countries, which one among them brought up the offer. Which I guessed to either be China or Russia.
No, this was not how BRICS was formed, it was neither China or Russia that came up with the idea, they weren't even the ones that came up with that acronym. From what i could garner online, it was Jim O'Neill, a Goldman Sachs economist that came up with the acronym BRIC, he used it to recognize four countries with very fast growing economies that (according to him), could rival the economic powerhouses like the U.S and others from the West.
These four countries found the idea interesting and decided to make a group from it, South Africa later joined them and it became BRICS.
I do not agree with you. Jim O'Neill did not proposed the establishment of BRIC, although he coined it. There is something the internet is not telling you about how BRICS was formed. It is possible that either China or Russia saw it as an advantage to reduced the economic power and sanction effect of the United States used it as an opportunity.
I found this about BRICS:
The organization seeks to deepen economic cooperation between the member countries and stand in contrast to the Western sphere of power.
BRICS sees itself as countering the traditional Western-led global order, with some member states viewing the organization as a way to boost their influence around the world.
China and Russia among the countries that joined can mostly have this motive, while others will instead have other motives that can help the economy of their countries. Another country that is among them that I think can have such motive is Iran but the country join in 2024 or so.
This is not about reality and not only what is read on the news or Internet.