It's pretty easy for recycling centers to sort out most of the glass and metal from that stream and then as technology improves they can sort and recycle even more of the plastic.
As for the food waste, I just assumed it was mostly destroyed by the recycling process. The high temperatures for metal and glass recycling make that seem easy to me. Plastic would be harder, but I think that's also part of the reason plastic can only be recycled a couple of times (it's not "pure" after it's recycled.)
Biological Treatment: Organic waste, including food waste, is often separated either at the beginning of the process through manual sorting or through processes like anaerobic digestion. In some facilities, organic waste is processed separately to produce compost or biogas.
If it were economic to really recycle it, China wouldn't have stopped taking ours. And most of the rest of Asia followed suit, which is why municipalities are sheepishly hoarding it in warehouses now without a plan, or just admitting to themselves (if not their citizens) it's a sham and diverting most of those plastics we put in the blue bins straight to the landfill.