I’ve heard multiple times that it’s not okay to allow any food to go down the drain even with a garbage disposal, I guess because solids shouldn’t go down the drain. But we put a shit ton of solids down the drain through the toilet and that seems to be fine. Does the toilet go to a different sewage pipe then the sink? Or does shit have different properties that make it dissolve better?
Your link isn’t too helpful for what you’re describing.
All household wastewater (including kitchen) ultimately goes into the sanitary sewer in most places, if it comes out of a house it’s all called “sanitary”. The alternative to sanitary sewer is storm drain, which is intended ONLY for surface rainwater and usually never have any household hookups, except potentially from rain gutters on the roof or tile drainage below ground, but municipalities are often pretty strict about that as these systems are very important for managing stormwater and avoiding flash flooding.
The third option, which I think is what you’re getting at, is called graywater, and indeed you could have sinks and even showers plumbed into graywater drains, but never toilets, and it’s often clean enough or can be filtered so that it can be re-used for flushing toilets, irrigating lawns and gardens or other forms of non-potable re-use that won’t be bothered by things like soaps and lotions and bacteria and other things that might get rinsed off. This is common for RVs and boats and other situations where fresh water might be scarce, but very much less typical for household plumbing in most places in my experience, and there is rarely any municipal system hookup for it and the graywater is usually intended to be used on-site within the household plumbing system itself, but it can help divert or reduce wastewater into the sanitary sewer and can help reduce the use of clean potable water, so it is a good thing in general.