Of course whether that happens depends a lot on where you're living.
The two largest sewerage treatment plants also capture and generate electricity from biogas [2].
[1] https://www.yvw.com.au/faults-works/planned-works/completed-...
[2] https://www.melbournewater.com.au/water-data-and-education/e...
And tbh not treating organic waste as some form of resource should be considered a scandal these days, and the only valid discussion to be had should be how to use it (my bet would be that in the long term that will be chemicals and not energy). There is legitimately a lot of talk about the landuse issues of bioenergy, but using organic waste doesn't have any of those problems. It should be an absolute nobrainer.
Household waste either goes to commercial composting plants (where the methane produced most likely escapes) or to sanitary landfills, where the reduced biological activity means that the scraps degrade at a much slower rate, but do eventually reduce to methane and other lipids, though possibly at the scale of millennia or longer.
