Ideally into your sewage system, as they are now concentrated wastewater (although if you live in a developed region with centralized water treatment, there won't be that much waste in the water to begin with). RO systems designed for processing seawater have a much harder time of it, as their waste is ultra-salty brine which will kill any local marine ecosystems if you decide to just dump it back into the sea.
Since the flow of deionized water is only 1/10 of total water flow... I think the increase in "waste" concentration is also only about 10% even of the filtered water is perfectly pure. So if you had 400ppm total dissolved solids it would now be *10/9=444ppm. Not much of a concern.
Seems like thie brine from desalination plants should be pumped into tailing ponds and dried out to get useful minerals out of it that could then be sold to help offset the cost and environmental impact of desalination. https://news.mit.edu/2019/brine-desalianation-waste-sodium-h... looks like this is not an original idea :)
Yes, the only problem is that most homes are not plumbed for grey water and it's a very expensive retrofit. If you're building a new home, ask about that and structured wiring. It's unfortunately usually a way more economical idea to just get those toilets that have a sink built into the top (popular in countries like Japan) that use the hand washing water to flush the toilet vs trying to store and/or pump it around.
