The thing that irks me a bit is that most of all that separation to "recycling, compost, trash" is mostly for virtue signalling anyway, from both the store and customers. "Early era" recycling made a lot of sense, where the effort to separate high value, easy-to-decontaminate items (like aluminum cans and glass bottles) made sense. The economics and ecological aspects never made much sense once we went to large scale single stream recycling, but China's willingness to be the world's garbage can postponed that for a bit.
I think it would make a lot more sense if the bins were just "glass bottles", "aluminum cans" and "everything else", but then people would feel less good about all the stuff they throw away.
Frankly, glass isn't worth recycling either. It's heavy, making it expensive to haul around, and the energy savings vs. using new silica is minimal at best, even without taking the extensive processing required to make it clean enough to use again in to account. Locally, crushed glass is used as landfill cover, which is a good use for it. But there is far more glass than there is a market for it.
Aluminum is absolutely worth it, due to the crazy-high energy requirements of otherwise separating it from oxygen during ore processing. And we do a very good job of lead recycling- something like 99%+ of lead from lead-acid batteries is recovered, which (IMO) shows that things like core charges work great.
In general, though, consumer-level recycling isn't the good that people think it is. What is needed is inexpensive trash collection and sanitation infrastructure. Make it too expensive, and people just illegally dump, which causes huge problems.
This isn't as exciting for most people to talk about compared to recycling, but that doesn't make it not true. The reason that 9o% of the plastics in the world's oceans come from a few rivers in asia isn't because of plastics per se, for example- it's because the cities along these rivers have zero waste management beyond 'throw it in the river and call it a day'. Collecting and burying plastics in a managed landfill is a perhaps-surprising solid ecological choice. Plastics make for strong and light packaging, and there's a real carbon cost in hauling things around. And the carbon in the plastic in a landfill somewhere isn't going anywhere.
Final note: doing a proper accounting of what actually is the best method of dealing with a waste stream is really, really hard, and I don't blame anyone for making what turn out to be incorrect assumptions, even when trying to do the right thing based on the current best evidence. All we can do is learn from it and try again.
I think it would make a lot more sense if the bins were just "glass bottles", "aluminum cans" and "everything else", but then people would feel less good about all the stuff they throw away.