That makes it sound as if the feces are just flushed out into nature, which is very far from my understanding.
Of course the purpose of a sewage treatment plant is to remove as much as possible of the material in the water, regardless of what it is, ending up with water that is as pure as possible so it can be let out into nature.
A large part of the US depends on septic systems. After flushing, the water, feces, and toilet paper all end up in a tank on the property. The toilet paper and feces there dissolve into the water thanks to bacterial action and other processes, and then eventually flows into a field line that distributes the water into the soil. This is entirely a passive process that can go decades without maintenance, though newer designs in wetter areas sometimes have a pump that sprays the water on the surface after chlorinating it.
My understanding is that the solids are separated from the liquids and in the case of the MWRD of Chicago [0], air dried before being put to reuse.
The point is TP just becomes part of the solids and there's no need to separate it from the rest of the solids, it's complementary being derived from trees.
Of course the purpose of a sewage treatment plant is to remove as much as possible of the material in the water, regardless of what it is, ending up with water that is as pure as possible so it can be let out into nature.