This recent WFR item could be useful:
https://resources.wolframcloud.com/FunctionRepository/resources/MinimalSubsets
It can be accessed as ResourceFunction["MinimalSubsets"]
ResourceFunction["MinimalSubsets"]
--- edit ---
Actually you seem to want ResourceFunction["MaximalSubsets"]
ResourceFunction["MaximalSubsets"]
https://resources.wolframcloud.com/FunctionRepository/resources/MaximalSubsets
---end edit ---
For a description of the BCL algorithm used by @Carl Woll in those WFR functions, and other ways to solve the problem, check this MSE post.
