Not really. It’s an alliance of rising imperial forces against the Americans dollar with the goal of creating a multipolar world, but I wouldn’t say that’s inherently more stable than one very powerful empire dominating everything. If anything, the neoliberalism mandated by global capitalism America championed is why the world became so unstable.
The extreme inequality causes artificial scarcity which drives people towards extreme nationalist ideologies. The increased nationalism that makes countries like China, Russia, and India more dangerous is thanks to that global economic system which encourages the worst in humanity. Local efforts at controlling capital are inherently undermined by it, as economic incentives demand fewer protections to compete with the rest of the world.
BRICS isn’t responsible for that, and if anything the deepening of economic ties between these empires will encourage them to seek peace with each other. As America becomes less and less relevant, the old tensions between those countries might cause it to collapse, but that won’t be the fault of it. Rather than it increasing or decreasing stability, it’s just a symptom of change rather than a driving force.
Multipolarity was inevitable and could have happened more peacefully with US leadership that understood their limitations and didn’t fight violently over the change. It won’t happen now, but that’s on the US for descending into chaos.