The regular trash doesn’t get separated, it’s just dumped. There’s also almost no restrictions on what can go in there, our trash cans are massive, and we have to pay for recycling, so many people just don’t bother (and a second trash can is not much more than a recycling bin).
We do have a recycling service that accepts most plastics (#1-#7), and they claim to recycle it, but they have pretty strict standards (needs to be clean, need to separate caps from bottles/jugs, etc), so I wouldn’t be surprised if most of it just ends up at the landfill anyway. Our area is a “single sort” facility, meaning people just dump everything into one bin and they sort it on their end. This means workers are even more likely to just throw stuff out that isn’t easily identifiable as recyclable.
One big issue is that they don’t accept glass, so to recycle glass, you need to take it somewhere special. I’m pretty obsessive about recycling, so I go out of my way to recycle everything I can (I have a bag of dead batteries in the garage, I make regular trips to recycle glass, etc), but I highly doubt most people bother. In fact, I have a few neighbors with 2 garbage cans and no recycling can.