Here are some ideas from abroad that you might like to run past your local supermarkets.
Living as I do practically on the border between Denmark and Germany I shop in both countries. In both, nearly all soft drinks, beer cans and bottles come with a deposit, so you hand them back in to the supermarket and get your deposit back. Those that don't carry a deposit go into either the plastic or the metal side of our recycling bin that is emptied once a fortnight.
In our municipality used batteries can be put on top of the recycling bin in a see-through plastic bag; in Germany shops have cardboard containers for batteries, and provide disposal bins marked off in sections for rubbish, cardboard and paper, and plastics. Aldi in Germany supply a bin at their vegetable counter for surplus cabbage leaves and the like. In Denmark glass bottles go into the recycling bin at home too; in Germany you have to transport them to the nearest bottle bank and sort them according to colour. There are however plenty of these bins.
All carrier bags sold in Aldi, Lidl, Coop, Penny Markt etc. are made of cloth or recyclable plastic. Most dress and shoe shops have reverted to paper carrier bags. Chemist's shops accept medicine back if you no longer need it, and various opticians and charities collected used spectacles.
Used clothes and shoes can be put in the nearest bin, emptied regularly by a charity, or handed in to a charity shop.
All plastics that have not been in direct contact with food go into the recycling bin, the refuse collecting company then sorts further. Anything that has contained food goes into the kitchen rubbish.
Paint, chemicals, electric equipment, old tools and garden waste the householder has to transport to the dump, or pay to have removed.
Our refuse disposal companies decide whether a bottle top is recyclable or not, so it is possible to run these companies at a profit without expecting the ordinary householder to have a degree in biochemistry and able to distinguish between the one and other type of plastic.
I think one of the ways forward is to shop in shops that are willing to use less packaging and only environmentally friendly packaging.
I have never understood why cucumbers and other foodstuffs that we wash or peel, or both, before using need to be wrapped in plastic.