I have mulched the dickens out of my beds this year - put down cardboard with a thick layer of pine needles - so far so good on no weeds in my veggie beds.
As for the walkways/outer edge, my biggest issue is “wire” grass. It’s invasive & all but impossible to pull up (or hoe). The roots stay in the ground & it’s back in a flash. I do have wood chips down as mulch around the beds/walkways & most weeds, other than the wire grass, pull right up. If I can get a hot, sunny day (today was pretty good), then ACV/Epson salt/Dawn works fairly well on almost everything.
Yeah that grass is a stinker long roots. We went through that for awhile our only solution is to just till and till and till and rake it all out.