Proper sourdough has a great shelf life.
I bake my own and have a linen bag I put them in before going in the bread bin and it’ll be good for 2/3 days as sandwiches and up to a week for toast - not that it ever lasts that long.
I have heard that a lot of supermarkets are making fake sourdough and that may be why it’s not lasting.
Real sourdough bread should only have 3 ingredients - flour, water, salt. If it’s got more than that (ie Yeast) then it’s just tricking you and you get the worst of both worlds because you don’t get the health benefits of the natural leavening and you don’t have the preservatives of traditional supermarket bread.
At the end of the day though… just eat what tastes nice to you.