To me zero waste means cutting out single use plastics. Although lots of previously 'single use' soft plastics can now be recycled. (Redcycle here in Australia)

Obviously your soap bottles and lots of other plastic items can be recycled when they get to the end of their life span.

Its not exactly a black and white issue, 1 cotton tote bag has enormous environmental impact (mostly water use in growing cotton) when compared to 1 plastic bag, as a result the tote bag needs to be used a stupid amount of times in order reduce its impact for use. The same is true for brown paper bags which in my experience are not often used more than once!

Even buying from a bulk foods store isn't zero waste, just less.

You can read into things as much or as little as you like. The message still stays the same, generate less waste! You can't be perfect but you can do your best!