I'm becoming a big fan of literal t-shirt bags. Cut the sleeves off, sew the shoulders so they don't fray, sew the torso opening, do something with the neck hole if needed. It's maybe 5 minutes of work and 50 cents at the local donation store. Now you have a cool, fairly customized bag you can make from various sizes.
Compact, washable, light-weight, strong and cheap.
Friendly reminder that glass contains no plastic. And recycling glass still requires virgin glass.
And that reusing glass requires very little energy. Switch to glass. Use deposit programs. If you don't have a deposit program, lobby your representative to tax single-use plastic and single-use aluminum, and establish a glass deposit system.
It's true, and it's problematic, but the plastic lining in an aluminium can is super thin, since it doesn't need to be structural. As far as resource use goes, it's still way better. It's best to look for improvements, and not to let the search for perfection block you from a marginal gain.
If you're going to re-use, use glass, where possible. If you're not, aluminium is still the better choice.
We should have higher deposits on cans and bottles. Here, it's been pegged at 5 cents since the 90s - it should be more like 25 cents now for cans, or a dollar for glass bottles.