right, so the functionality of BRICS is a counter-west/colonialism/anglo-saxon kind of organization. It's seeking for a different economic order. China & India's interest are aligned on this although they hope different outcomes from it. Having India in BRICS simply just increases the attractiveness as a anti-west organization rather than just one where you follow China's orders. That's far more palatable for other countries. And also give those countries a cover since they are not just joining a China/Russia alliance but rather one with all the major global south countries. Just watch how the importance given to Brazil at NDB has given a lift to its relevance for Latin American countries. If you seek to replace IMF and world bank, then China has to hide a little bit behind its cover.Both BRICS and SCO were formed at a time that the world is a lot different. Beside, China never wanted to invite India to SCO in the first place but Russia insisted that India should be invited to counter weight China's growing influence which China was forced to accept but also asked Pakistan to join. By the time both India and Pakistan have joined the SCO security pact, SCO has become irrelevant. Archrival such as India and Pakistan can't join the same group of framework that is dedicated to security without rendering any security agreement impossible to agree and progress. Unlike BRICS, SCO had more potential to form an alliance to counter the West if India didn't join.
As for BRICS, I doubt China would have predicted India would choose a path of populist policies and leaders. Modi is a populist leader that doesn't care much for pragmatism or long term planning. China is working to expand BRICS to dilute India's influence to the BRICS. By creating BRICS bank in Shanghai, China has ensured that India has little say in many future economic cooperation or framework. In the end of the day, China has money and India doesn't have money. Other political and diplomatical agreements probably can progress as most nations just want to shield themselves from G7 and Western powers' hegemony and abuse of powers and financial sanctions.
I doubt BRICS can be formed as anti-American alliance even if India didn't join. Most countries just don't want to choose a side in the future power struggle between the US and China. However, it is quite possible BRICS can develop into a pact that could ensure any Western sanctions would become irrelevant. BRICS might be able to provide an alternative to the Western financial hegemony that countries would have a choice other than IMF and World bank that imposed Western policies and will and interests onto any borrowing countries and forced them to accept radical and painful reforms or disposed state owned assets.
Everyone knows when they come to NDB in Shanghai that China is the real power behind BRICS, but as long as India doesn't do anything self-destructive, BRICS will continue to serve both countries.