Connecting battery packs in parallel and series, each with their own BMS
It depends, but generally, no except for testing.

BMCs tend to switch off the battery when over-charged, over-loaded, over-discharged, over-heated or when it just feels like to.

Think about over-discharging: you will never get them to switch off together. The first one switching off in a parallel pack will transfer the load to it's peers, eventually overloading them. The first parallel pack to turn off will get all the voltage of the other two packs in reverse. Will it survive?

Then, charging is another sad story. I don't know if s8232A tries to ballance the cells, but if it does, every one of them will ballance just the cells it is connected to - and by doing so, it will load it's parallel peers down from ballance with their serial counterparts. Completely counter-productive.

Some BMS modules can be chained together in order to function as one large BMS. They generally need external connections and generally, external logic. s8232A is not one of them.

p.s. I checked - there is no ballance logic in s8232A. But still no happines at other points.