Livestock farmers have been doing this for decades. However they have very different constraints. It doesn't matter if a little of one gets mixed with the other - in fact they need enough water in the solids for proper decomposition. Both are normally pumped as well, so the solids are generally expected to be more a viscous liquid than actual solids. They don't want too much water in some stages, but they have plenty of room for a large setteling tank (read gravity works for them). They are also dealing with far more waste than a space mission, so they need something that is efficient/cheap at quantity.

GP is saying that was previously required, not that it was invented. The new one can handle the mixture; not necessarily (presumably not?) by separating it.